PAGE 1: Overview OVERVIEW ======== Plane figures are flat shapes. In this sub-strand you will name rectangles, squares, triangles, circles and ovals on objects around you, draw them, and find lines of symmetry by folding. You will make patterns with squares, rectangles and triangles, and test the properties of those shapes. ## Strand 3.0: Geometry Sub-strand 3.3: Plane Figures Suggested lessons: 6 ## What this sub-strand covers • Rectangles, squares, triangles, circles and ovals • Lines of symmetry • Properties of plane figures ## Source • KICD Grade 4 Mathematics Curriculum Design (Revised 2024) — Strand 3.0 Geometry, Sub-strand 3.3 Plane Figures ## Learning outcomes By the end of the sub-strand, the learner should be able to: a) identify rectangles, squares, triangles, circles and ovals from objects in the environment b) draw the shapes of rectangles, squares, triangles, circles and ovals from objects in the environment c) identify lines of symmetry of different shapes d) make patterns using squares, rectangles and triangles e) identify properties of plane figures in different situations f) appreciate using shapes in real-life situations ## Key inquiry questions 1. How can you make patterns using shapes? PAGE 2: How we will learn ## Learning experiences • discuss and recognise shapes of rectangles, squares, triangles, circles and ovals from common objects in the environment • sketch the shapes of rectangles, squares, triangles, circles and ovals in their books or charts using objects in the environment • discuss and fold the shapes into two equal parts and recognise the fold line as the line of symmetry • discuss how many lines of symmetry can each shape possibly have by folding the shapes • work with peers to make patterns using squares, rectangles and triangles • identify the properties of a square practically • discuss the properties of a rectangle practically • identify properties of a triangle practically • collaboratively use digital devices to learnmore about plane figures and make patterns ## Core competencies • Creativity and imagination: learner explores new ideas while making patterns using squares, rectangles and triangles. ## Values • Respect: learner displays humility while recognising shapes of rectangles, squares, triangles, circles and ovals from common objects in the environment. ## Pertinent and contemporary issues • Peer Education and Mentorship: learner exhibits teamwork while sketching the shapes of rectangles, squares, triangles, circles and ovals from objects in the environment. ## Links to other learning areas • The learner is able to relate making patterns using squares, rectangles and triangles to perspective in Creative Arts. PAGE 3: Lesson 1: Rectangles, squares, triangles, circles and ovals — Five shapes LESSON 1: RECTANGLES, SQUARES, TRIANGLES, CIRCLES AND OVALS =========================================================== ## What you will learn • Name a rectangle, square, triangle, circle and oval. • Identify these shapes on objects in the environment. Curriculum outcomes: a) identify rectangles, squares, triangles, circles and ovals from objects in the environment; f) appreciate using shapes in real-life situations ## Introduction The cover of your exercise book, a floor tile, a coin and a set square are different shapes. Naming the flat shape you see helps you describe an object so that someone else can picture it. ## Notes A plane figure is a flat shape. You can draw it on a page. A box is a solid, so the box itself is not a plane figure, but each flat face of the box is one. ### Five shapes - A rectangle has 4 straight sides and 4 square corners. Each pair of opposite sides is equal. - A square has 4 straight sides that are all equal, and 4 square corners. A square is a special rectangle: its opposite sides are equal and its corners are square, and its sides happen to be all the same length. A rectangle whose sides are not all equal is not a square. - A triangle has 3 straight sides and 3 corners. - A circle is perfectly round. It has no corners and no straight sides. The centre is the middle, and every point on the edge is the same distance from the centre. - An oval is a curved shape with no corners. A stretched circle that is the same at both ends is an oval. An egg is an oval that is narrower at one end than at the other. PAGE 4: Lesson 1: Rectangles, squares, triangles, circles and ovals — Notes 4 ### Look at the face, not the whole object The cover of an exercise book is a rectangle. Some floor tiles and handkerchiefs are squares. The face of a set square is a triangle. A coin, a clock face and a bottle top are circles. An egg, seen from the side, is an oval. A dice is a cube, and each of its six faces is a square. A chalk box is a cuboid, and its faces are rectangles. A round plate gives a circle. Turn the object and you may see a different face, so say which face you mean. Shapes help people plan real things. A door is a rectangle so that it fits the frame. Tiles are often squares or rectangles so that they fit with no gaps. A round wheel is a circle so that it rolls. When you name the shape, you are describing how the object can be used. [DIAGRAM] TYPE: svg ALT: Five plane figures: rectangle, square, triangle, circle and oval. PAYLOAD: CAPTION: Five plane figures: rectangle, square, triangle, circle and oval. [/DIAGRAM] PAGE 5: Lesson 1: Rectangles, squares, triangles, circles and ovals — Shape hunt ## Key words • plane figure — a flat shape, such as a rectangle or a circle • square — a rectangle whose four sides are all equal • oval — a curved shape with no corners, like a stretched circle or an egg ## Worked examples ### Example 1 A window frame has 4 straight sides, opposite sides equal, and 4 square corners. The long sides are not the same length as the short sides. What shape is the frame? Working: 1. 4 square corners and opposite sides equal make a rectangle. 2. The sides are not all equal, so it is not a square. Answer: A rectangle ## Worked examples ### Example 2 How many corners do 6 triangles have altogether? Working: 1. Each triangle has 3 corners. 2. 6 × 3 = 18. Answer: 18 ## Worked examples ### Example 3 A square tile has 4 equal sides. How many sides do 8 separate tiles have before they are joined? Working: 1. Each tile has 4 sides. 2. 8 × 4 = 32. Answer: 32 ## Activity: Shape hunt You will need: Exercise book, Objects in the classroom such as books, coins, tiles, a set square and a box 1. In a group, look at common objects and name the plane figure of each face you can see. 2. Make five columns: rectangle, square, triangle, circle, oval. 3. Write each object in the column of its shape. If a box shows rectangles, record the face, not the whole box. 4. Find at least one example of each shape, or say honestly if the oval is missing and where you might see one, such as an egg. 5. Tell another group why a square can also be called a special rectangle. ## Practice 1. How many straight sides does a triangle have? 2. A floor tile has 4 equal sides and 4 square corners. What shape is it? 3. Name the shape of a coin. 4. How many corners are there on 5 separate square tiles? ## Answers to practice 1. 3 2. A square 3. A circle 4. 20 ## Summary • A plane figure is a flat shape. • A square is a special rectangle with all sides equal. • Name the face you are looking at: a book cover, a coin, a tile or an egg. PAGE 6: Lesson 2: Drawing shapes from objects LESSON 2: DRAWING SHAPES FROM OBJECTS ===================================== ## What you will learn • Sketch a rectangle, square, triangle, circle and oval from an object. • Check that a triangle's sides are long enough to meet. Curriculum outcomes: b) draw the shapes of rectangles, squares, triangles, circles and ovals from objects in the environment ## Introduction Put a book, a square tile, a set square, a bottle top and an egg on the desk. A sketch copies the flat shape of each one into your book so that the drawing can be checked when the object is put away. ## Notes To sketch a shape, look at one flat face and draw what you see. Use a ruler for straight sides. Use your right angle tester for square corners. ### Rectangle and square For a rectangle, draw two pairs of opposite sides. The opposite sides must be equal, and every corner must be a square corner. If the long side is 8 cm and the short side is 3 cm, the distance all the way round is 8 + 3 + 8 + 3 = 22 cm. For a square, all four sides must measure the same. A square of side 5 cm has a distance all the way round of 4 × 5 = 20 cm. If your drawing has one side longer than the others, it is a rectangle that is not a square. Measure before you colour it. PAGE 7: Lesson 2: Drawing shapes from objects — Circle and oval ### Triangle Draw three straight sides that join at three corners. The sides must be able to meet. Two sides together must be longer than the third side, or the ends cannot reach. Sides of 3 cm, 4 cm and 5 cm do meet, because 3 + 4 = 7, and 7 is longer than 5. Sides of 2 cm, 3 cm and 6 cm do not meet, because 2 + 3 = 5, which is shorter than 6. Trace a set square if you need a triangle that already closes. ### Circle and oval A circle is hard to draw freehand and stay round. Trace a coin, a bottle top or a roll of tape. Mark the centre lightly. An oval can be traced from an egg or from an oval lid. Do not press a sharp point into an egg. If you have no oval object, draw a closed curve that is longer than it is wide and has no corners, then say whether your sketch is the same at both ends. Label each sketch with the name of the shape and the object you copied. ## Key words • sketch — a drawing that shows the shape of an object • centre — the middle point of a circle ## Worked examples ### Example 1 A rectangle is 8 cm long and 3 cm wide. What is the distance all the way round? Working: 1. Opposite sides are equal, so the sides are 8 cm, 3 cm, 8 cm and 3 cm. 2. 8 + 3 + 8 + 3 = 22. Answer: 22 cm ## Worked examples ### Example 2 Can a triangle have sides of 2 cm, 3 cm and 6 cm? Working: 1. The two shorter sides add up to 2 + 3 = 5. 2. 5 is shorter than 6, so the ends cannot meet. Answer: No ## Worked examples ### Example 3 A square tile has sides of 5 cm. What is the distance all the way round? Working: 1. A square has 4 equal sides. 2. 4 × 5 = 20. Answer: 20 cm PAGE 8: Lesson 2: Drawing shapes from objects — Answers to practice ## Activity: Sketch the objects You will need: Ruler, Right angle tester, Book, square cut-out, set square, bottle top or coin, Exercise book 1. With a partner, choose one object for each shape: rectangle, square, triangle, circle and oval. 2. Sketch each face in your book using a ruler for straight sides. Trace the round objects. 3. Measure the sides of the rectangle and the square. Check the square corners with the tester. 4. Try to draw a triangle with sides 2 cm, 3 cm and 6 cm, then one with sides 3 cm, 4 cm and 5 cm. Record which one closes. 5. Swap books and check that each sketch is labelled with the shape name. ## Practice 1. A square has sides of 9 cm. What is the distance all the way round? 2. A book cover is 20 cm long and 15 cm wide. Is the cover a square? 3. Do sides of 3 cm, 4 cm and 5 cm make a triangle? 4. What object can you trace to draw a circle? ## Answers to practice 1. 36 cm 2. No. It is a rectangle, because 20 cm is longer than 15 cm. 3. Yes, because 3 + 4 = 7, which is longer than 5, and the other pairs are longer still. 4. A coin, a bottle top or another round lid. ## Summary • Use a ruler for straight sides and a right angle tester for square corners. • All four sides of a square are equal. Opposite sides of a rectangle are equal. • Two sides of a triangle must together be longer than the third side. PAGE 9: Lesson 3: The line of symmetry — A fold that works LESSON 3: THE LINE OF SYMMETRY ============================== ## What you will learn • Fold a shape into two matching parts. • Name the fold as a line of symmetry when the parts match. Curriculum outcomes: c) identify lines of symmetry of different shapes ## Introduction Fold a paper square so that one edge lands exactly on the opposite edge. The two parts lie on top of each other. The crease is a line of symmetry. ## Notes A line of symmetry is a fold line that splits a shape into two parts that match. One part is the mirror of the other. If you fold along that line, every corner and every edge of one part lands on the other part. ### A fold that works Cut out a rectangle, a square, a triangle, a circle and an oval from used paper. Fold the square so that one side lies on the opposite side. The crease goes through the middle, and the two halves match. That crease is a line of symmetry. Open the paper and draw a dashed line along the crease so you can see it. Fold the same square from one corner to the opposite corner. The two triangular parts match. That diagonal crease is also a line of symmetry of the square. ### A fold that does not work Fold a rectangle that is not a square from one corner to the opposite corner. The sides do not land on each other, because the long side is longer than the short side. That crease is not a line of symmetry, even though it cuts the paper into two pieces. Cutting into two pieces is not enough. The pieces must match. PAGE 10: Lesson 3: The line of symmetry — Half of the shape ### Half of the shape A line of symmetry gives two equal parts. If a square is drawn as 16 small equal squares, in 4 rows of 4, each matching half has 16 ÷ 2 = 8 small squares. You can check a fold by counting. If one side of the crease has more of the shape than the other, the crease is not a line of symmetry. Some shapes have no line of symmetry. A triangle with three sides of different lengths will not match on any fold. Try the folds before you decide. [DIAGRAM] TYPE: svg ALT: A square matches on a middle fold and on a diagonal. A diagonal of a non-square rectangle does not give matching halves. PAYLOAD: CAPTION: A square matches on a middle fold and on a diagonal. A diagonal of a non-square rectangle does not give matching halves. [/DIAGRAM] PAGE 11: Lesson 3: The line of symmetry — Example 2 ## Key words • line of symmetry — a fold that makes two matching halves • match — to lie exactly on top of another part, with nothing sticking out ## Worked examples ### Example 1 A paper square is made of 16 small equal squares. It is folded on a line of symmetry. How many small squares are in each half? Working: 1. The two halves match, so each has the same number. 2. 16 ÷ 2 = 8. Answer: 8 ## Worked examples ### Example 2 You fold a rectangle that is not a square along a diagonal. The long side does not land on the short side. Is the diagonal a line of symmetry? Working: 1. The two parts do not match. 2. A line of symmetry must give two matching halves. Answer: No ## Worked examples ### Example 3 Two matching halves of a shape have 6 square units each. How many square units are in the whole shape? Working: 1. The whole shape is the two halves together. 2. 6 + 6 = 12. Answer: 12 ## Activity: Fold and find the crease You will need: Paper cut-outs of a square, a rectangle that is not a square, a triangle, a circle and an oval, Pencil 1. Fold the square so that opposite sides match. Open it and draw a dashed line on the crease. 2. Fold the square corner to opposite corner. If the parts match, draw that line too. 3. Fold the non-square rectangle corner to opposite corner. Record whether the parts match. 4. Fold the circle through the centre and the oval along its length. Say which creases are lines of symmetry. 5. Compare folds with a partner before you decide. PAGE 12: Lesson 3: The line of symmetry — Summary ## Practice 1. What is a line of symmetry? 2. A shape has 18 equal small squares and is folded on a line of symmetry. How many small squares are in each half? 3. Each matching half of a shape has 7 square units. How many square units are in the whole shape? 4. Does cutting a shape into two pieces always make a line of symmetry? ## Answers to practice 1. A fold line that splits a shape into two halves that match. 2. 9 3. 14 4. No. The two pieces must match when folded. ## Summary • A line of symmetry is a fold that makes two matching halves. • The diagonal of a square is a line of symmetry. • The diagonal of a rectangle that is not a square is not a line of symmetry. LESSON 4: HOW MANY LINES OF SYMMETRY? ===================================== ## What you will learn • Find how many lines of symmetry a square, a rectangle, a triangle, a circle and an oval can have. • Use folding, not guessing, to decide. Curriculum outcomes: c) identify lines of symmetry of different shapes ## Introduction A paper circle can be folded in many ways and still match, as long as the crease goes through the centre. A triangle with three different side lengths may not match on any fold. The number of lines of symmetry depends on the shape. ## Notes Fold each cut-out in every way that might match. Draw only the creases that work. Then count them. ### Square and rectangle A square has 4 lines of symmetry: one fold through the middles of the top and bottom sides, one through the middles of the left and right sides, and two folds from corner to opposite corner. A rectangle that is not a square has 2 lines of symmetry. Both go through the middles of opposite sides. Its diagonals are not lines of symmetry. ### Triangles Count the equal sides. - If all 3 sides are equal, there are 3 lines of symmetry. Each one goes from a corner to the middle of the opposite side. - If exactly 2 sides are equal, there is 1 line of symmetry. It goes from the corner between the equal sides to the middle of the other side. - If all 3 sides are different, there is no line of symmetry. PAGE 13: Lesson 4: How many lines of symmetry? — Example 3 ### Circle and oval Every fold of a circle through the centre is a line of symmetry. There are more of them than you can count: turn the paper a little and fold through the centre again. An oval that is the same at both ends, like a stretched circle, has 2 lines of symmetry. One runs along the length and one runs across the middle. An egg is narrower at one end. It has only 1 line of symmetry, from the narrow end to the wide end. A fold across the middle of an egg does not match, because the two ends are different. Write the number next to each shape after the group agrees. Do not say a rectangle has 4 lines unless you have checked that all its sides are equal. ## Key words • equal sides — sides that are the same length • diagonal — a straight line from one corner of a shape to the opposite corner ## Worked examples ### Example 1 How many lines of symmetry do 3 squares have altogether? Working: 1. Each square has 4 lines of symmetry. 2. 3 × 4 = 12. Answer: 12 ## Worked examples ### Example 2 A rectangle that is not a square has 2 lines of symmetry. How many lines of symmetry do 5 such rectangles have altogether? Working: 1. Each one has 2 lines. 2. 5 × 2 = 10. Answer: 10 ## Worked examples ### Example 3 A triangle has all 3 sides equal. A square is drawn beside it. How many more lines of symmetry does the square have than the triangle? Working: 1. The triangle has 3 lines of symmetry. 2. The square has 4. 3. 4 − 3 = 1. Answer: 1 PAGE 14: Lesson 4: How many lines of symmetry? — Practice ## Activity: Count the matching folds You will need: Cut-outs of a square, a non-square rectangle, triangles with different side lengths, a circle and an oval, Pencil 1. Fold each shape in as many matching ways as you can. Draw a dashed line on each crease that matches. 2. Count the lines and write the number inside the shape. 3. Check the triangle by measuring or matching its sides first, so you know whether 3 sides, 2 sides or no sides are equal. 4. Fold the circle only through the centre, and record that there are more lines than you can finish drawing. 5. Compare counts with another pair and refold any shape you disagree about. ## Practice 1. How many lines of symmetry does a square have? 2. How many lines of symmetry does a rectangle that is not a square have? 3. A triangle has all sides different. How many lines of symmetry does it have? 4. An egg has 1 line of symmetry. A stretched circle that is the same at both ends has 2. How many more lines does the stretched circle have? ## Answers to practice 1. 4 2. 2 3. 0 4. 1 ## Summary • A square has 4 lines of symmetry. A non-square rectangle has 2. • A triangle has 3, 1 or 0 lines of symmetry, depending on how many sides are equal. • A circle has many lines through the centre. An egg has 1. PAGE 15: Lesson 5: Patterns with squares, rectangles and triangles — Planning a border LESSON 5: PATTERNS WITH SQUARES, RECTANGLES AND TRIANGLES ========================================================= ## What you will learn • Make a repeating pattern with squares, rectangles and triangles. • Count how many of each shape are in the pattern. Curriculum outcomes: d) make patterns using squares, rectangles and triangles; f) appreciate using shapes in real-life situations ## Introduction Floor tiles, fabric borders and drawn frames often repeat the same shapes in the same order. Once you know the part that repeats, you can count the shapes without building the whole pattern. ## Notes A pattern repeats in a regular way. The repeating part is the shortest piece that comes again and again. In square, triangle, square, triangle, the repeating part is square then triangle. It uses 2 shapes. Four repeats use 4 × 2 = 8 shapes, and half of them are triangles, so there are 4 triangles. ### Fitting without gaps Squares fit together with no gaps and no overlaps, like floor tiles. Rectangles do the same. Put two identical squares side by side and you make a rectangle. If each square has sides of 4 cm, the new rectangle is 8 cm long and 4 cm wide, because 4 + 4 = 8. Triangles can also make a pattern. A row of triangles pointing up, then a row pointing down, can fill a strip. Circles do not fit together without gaps, so a pattern of circles looks different from a tiled floor. This sub-strand asks you to build with squares, rectangles and triangles. ### Planning a border Suppose the repeating part is square, rectangle, triangle. That is 3 shapes. In 12 shapes there are 12 ÷ 3 = 4 repeats, so there are 4 squares, 4 rectangles and 4 triangles. Draw one repeat first. Then copy it. Check the count before you stick the cut-outs down. Patterns like these are used in art when someone plans a cloth border, a mat or a wall design. The mathematics is the repeat and the count. The art is the choice of order and colour. If a digital device is available, you and a partner can look at a shape pattern and copy the repeating part with paper. If there is no device, the paper cut-outs are enough. PAGE 16: Lesson 5: Patterns with squares, rectangles and triangles — Example 3 ## Key words • pattern — an arrangement that repeats in a regular way • repeating part — the shortest piece of a pattern that comes again and again ## Worked examples ### Example 1 A pattern repeats square, rectangle, triangle. There are 12 shapes in the pattern. How many triangles are there? Working: 1. The repeating part has 3 shapes and 1 of them is a triangle. 2. 12 ÷ 3 = 4, so there are 4 triangles. Answer: 4 ## Worked examples ### Example 2 A mat is made of 5 rows with 6 squares in each row. How many squares are used? Working: 1. Each row has 6 squares. 2. 5 × 6 = 30. Answer: 30 ## Worked examples ### Example 3 Two squares, each of side 4 cm, are placed side by side to make a rectangle. How long is the rectangle? Working: 1. The length is two sides joined. 2. 4 + 4 = 8. Answer: 8 cm PAGE 17: Lesson 5: Patterns with squares, rectangles and triangles — Practice ## Activity: Build a shape pattern You will need: Cut-outs of squares, rectangles and triangles, Glue or a pencil to draw round the cut-outs, Manila paper or an exercise book 1. With a partner, choose a repeating part that uses at least two of the shapes. 2. Make 4 repeats in a border. Count how many of each shape you used and check by multiplying. 3. Fill a small rectangle using only squares, with the same number in each row. 4. Make a second pattern in which two squares side by side stand for one rectangle. 5. If a device is available, compare your repeating part with a pattern you find there, then explain your own pattern to another group. ## Practice 1. The repeating part is square, square, triangle. How many shapes are in 5 repeats? 2. A floor has 4 rows of 7 rectangular tiles. How many tiles is that? 3. In a pattern of 12 shapes, every third shape is a triangle and the others are squares. How many squares are there? 4. Two squares of side 6 cm are joined side by side. How long is the rectangle they make? ## Answers to practice 1. 15 2. 28 3. 8 4. 12 cm ## Summary • The repeating part tells you how the pattern continues. • Number of shapes = number of repeats × shapes in one repeat. • Squares and rectangles can tile a surface with no gaps. PAGE 18: Lesson 6: Properties of squares, rectangles and triangles — Square LESSON 6: PROPERTIES OF SQUARES, RECTANGLES AND TRIANGLES ========================================================= ## What you will learn • Test the sides and corners of a square, a rectangle and a triangle. • State the properties you found. Curriculum outcomes: e) identify properties of plane figures in different situations; f) appreciate using shapes in real-life situations ## Introduction A property is something that is true of the shape every time, not just of one drawing. Measuring the sides and testing the corners tells you which properties you can trust. ## Notes Use a cut-out, a ruler or a piece of string, and a right angle tester. Match sides by laying them on top of each other if you have no ruler. ### Square A square has 4 sides and all of them are equal. It has 4 corners and each one is a right angle. It has 4 lines of symmetry. Because the sides are equal and the corners are right angles, every square is a rectangle. The distance all the way round a square of side 7 cm is 4 × 7 = 28 cm. ### Rectangle A rectangle has 4 sides. Opposite sides are equal. All 4 corners are right angles. If the sides are not all equal, it has 2 lines of symmetry, not 4. A rectangle that is 12 cm long and 5 cm wide has a distance all the way round of 12 + 5 + 12 + 5 = 34 cm. Doors, book covers and many windows use this property so that opposite edges match. ### Triangle A triangle has 3 straight sides and 3 corners. The sides may all be equal, exactly two may be equal, or all three may be different. Some triangles have one right angle. On a set square, one corner matches the tester and the other two are smaller than a right angle. PAGE 19: Lesson 6: Properties of squares, rectangles and triangles — Example 2 Here is a practical test. Draw a triangle on paper and tear off the three corners. Place the torn corners side by side. They make a straight line, and a straight line is 2 right angles. So the three corners of a triangle together make 2 right angles. If one corner is already a right angle, the other two together make 2 − 1 = 1 right angle. A circle is different: it has no straight sides and no corners. An oval has no corners either. Knowing the properties helps you choose a shape that will fit a job, such as a rectangular door or a triangular brace. ## Key words • property — something that is true of a shape, such as equal sides or right angles • opposite sides — sides that face each other in a rectangle or a square • right-angled triangle — a triangle with one square corner ## Worked examples ### Example 1 A square has sides of 7 cm. What is the distance all the way round? Working: 1. All 4 sides are equal. 2. 4 × 7 = 28. Answer: 28 cm ## Worked examples ### Example 2 A rectangle is 12 cm long and 5 cm wide. What is the distance all the way round? Working: 1. Opposite sides are equal. 2. 12 + 5 + 12 + 5 = 34. Answer: 34 cm PAGE 20: Lesson 6: Properties of squares, rectangles and triangles — Test the properties ## Worked examples ### Example 3 One corner of a triangle is a right angle. The three corners together make 2 right angles. How many right angles do the other two corners make together? Working: 1. The three corners together make 2 right angles. 2. One corner uses 1 of them. 3. 2 − 1 = 1. Answer: 1 right angle ## Activity: Test the properties You will need: Cut-outs of a square, a rectangle and several triangles, Ruler or string, Right angle tester, Scrap paper 1. In a group, measure or match the sides of the square and the rectangle. Record which sides are equal. 2. Test every corner with the right angle tester. 3. Sort the triangles into three sets: all sides equal, exactly two sides equal, and all sides different. 4. Tear the corners off one paper triangle and place them together. Say what they make. 5. Write three properties of the square, three of the rectangle and three of the triangle in your book. ## Practice 1. A rectangle is 9 cm long and 4 cm wide. What is the distance all the way round? 2. How many right angles do the corners of 4 squares make altogether? 3. A triangle has sides of 5 cm, 5 cm and 8 cm. How many of its sides are equal? 4. The three corners of a triangle together make how many right angles? ## Answers to practice 1. 26 cm 2. 16 3. Two sides are equal. 4. 2 ## Summary • A square has 4 equal sides and 4 right angles. A rectangle has opposite sides equal and 4 right angles. • A triangle has 3 sides and 3 corners. Its corners together make a straight line. • Test properties by measuring, matching sides and using a right angle tester. PAGE 21: Revision quiz REVISION QUIZ ============= Answer all the questions, then mark yourself on the Answers tab. 1. Which shape has 3 straight sides? A. Rectangle B. Circle C. Triangle D. Oval 2. A shape has 4 equal sides and 4 square corners. What is it? A. A rectangle that is not a square B. A square C. An oval D. A triangle 3. A rectangle is 6 cm long and 2 cm wide. What is the distance all the way round? 4. Which side lengths can make a triangle? A. 2 cm, 3 cm, 6 cm B. 3 cm, 4 cm, 5 cm C. 1 cm, 2 cm, 4 cm D. 2 cm, 2 cm, 6 cm 5. What is a line of symmetry? A. Any cut across a shape B. A fold that makes two matching halves C. The longest side D. A corner 6. How many lines of symmetry does a square have? A. 1 B. 2 C. 3 D. 4 7. How many lines of symmetry does a triangle with all sides equal have? 8. The repeating part of a pattern is square, rectangle, triangle. How many triangles are in 9 shapes? A. 2 B. 3 C. 6 D. 9 9. A design has 3 rows of 8 squares. How many squares is that? 10. Which is a property of every rectangle? A. All four sides are equal B. It has 3 corners C. Opposite sides are equal and the corners are right angles D. It has no straight sides 11. The three corners of a triangle together make a straight line. How many right angles is that? A. 1 B. 2 C. 3 D. 4 12. Why are square tiles useful for covering a floor? PAGE 22: Quiz answers ANSWERS ======= 1. C. Triangle A triangle has 3 straight sides and 3 corners. 2. B. A square Four equal sides and four right angles make a square. A square is also a special rectangle. 3. 16 cm The sides are 6 cm, 2 cm, 6 cm and 2 cm. 6 + 2 + 6 + 2 = 16. 4. B. 3 cm, 4 cm, 5 cm 3 + 4 = 7, which is longer than 5. For 2, 3 and 6, 2 + 3 = 5, which is shorter than 6, so those sides cannot meet. 5. B. A fold that makes two matching halves The two sides of the fold must match. A cut into two unequal pieces is not enough. 6. D. 4 A square matches on two middle folds and on both diagonals. 7. 3 Each line goes from a corner to the middle of the opposite side. 8. B. 3 There is 1 triangle in every 3 shapes. 9 ÷ 3 = 3. 9. 24 3 × 8 = 24. 10. C. Opposite sides are equal and the corners are right angles Every rectangle has opposite sides equal and 4 right angles. Only a square has all four sides equal. 11. B. 2 A straight line is a half turn, which is 2 right angles. 12. They fit together with no gaps, and each tile has equal sides and square corners. The equal sides and right angles let the tiles meet edge to edge.