Answer: (D) parallelLines that always stay the same distance apart and never meet are parallel.
3. Which pair of lines is perpendicular?1 mark
(A) B(B) A(C) C(D) D
Answer: (A) BPair B meets at a right angle (shown with the square corner in the answer key). A and D meet at other angles. C are parallel lines that never meet.
4. Which statement is true?1 mark
(A) Parallel lines meet at a right angle.(B) Perpendicular lines meet at a right angle.(C) Parallel lines meet at one point.(D) Perpendicular lines never meet.
Answer: (B) Perpendicular lines meet at a right angle.Perpendicular lines meet at 90°. Parallel lines never meet.
Section B · Write your answer 11 marks
5. Look at the lines MN and NK. Are they perpendicular? Write yes or no.1 mark
Answer: NoThe angle at N is not a right angle. MN is straight up but NK is slanted, so they are not perpendicular.
6. Which line is perpendicular to PQ?1 mark
Answer: RSPQ goes straight up and down. RS goes straight across and meets PQ at a right angle. VW is slanted. TU is parallel to PQ.
7. In the figure, which lines are parallel to one another?1 mark
Answer: CD, EF and GHCD, EF and GH are all straight across and never meet. AB is perpendicular to each of them.
8. Hana says, "AB and CD are not parallel because they are different lengths." Is she correct? Explain.1 mark
Answer: No. Parallel lines can be different lengths. They never meet.Parallel lines never meet and stay the same distance apart. Their lengths do not matter.
9. Which line is neither parallel nor perpendicular to AB?1 mark
Answer: EFGH is parallel to AB. CD is perpendicular to AB. EF is slanted, so it is neither.
10. (a) How many pairs of parallel lines are there in the figure? (b) How many pairs of perpendicular lines are there?2 marks
Answer: (a) 2 pairs (b) 4 pairs(a) PQ // RS and WX // YZ, so 2 pairs. (b) Each line going down meets each line going across at a right angle: 2 × 2 = 4 pairs.
11. Draw a line through P that is parallel to AB. Use a ruler.2 marks
Answer: Line through P that never meets AB, drawn straight across.Draw along the grid line through P. It stays the same distance from AB, so it is parallel.
12. Use a set square. Draw a line from M to line XY so that it is perpendicular to XY.2 marks
Answer: Line from M straight down to XY, meeting it at a right angle.Place the set square on XY with its right-angle corner at the line. Slide it until the edge touches M, then draw.
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Primary 4 Mathematics · Chapter 8 · Answers and explanations
Lesson 8.2: Properties of Rectangles (answers)
Section A · Multiple choice 4 marks
1. How many right angles does a rectangle have?1 mark
(A) 1(B) 2(C) 3(D) 4
Answer: (D) 4A rectangle has 4 right angles, one at each corner.
2. ABCD is a rectangle. What is the length of DC?1 mark
(A) 9 cm(B) 4 cm(C) 13 cm(D) 18 cm
Answer: (A) 9 cmOpposite sides of a rectangle are equal. DC is opposite AB, so DC = 9 cm.
3. PQRS is a rectangle. Which side is parallel to PQ?1 mark
(A) QR(B) SR(C) PS(D) none of the sides
Answer: (B) SRIn a rectangle, opposite sides are parallel. SR is opposite PQ. QR and PS are perpendicular to PQ.
4. Which statement about a rectangle is true?1 mark
(A) All four sides are equal.(B) Opposite sides are perpendicular.(C) Opposite sides are equal and parallel.(D) It has only 2 right angles.
Answer: (C) Opposite sides are equal and parallel.A rectangle has opposite sides that are equal and parallel, and 4 right angles. The four sides are not always equal.
Section B · Write your answer 11 marks
5. ABCD is a rectangle. Find the length of BC.1 mark
Answer: 7 cmBC is opposite AD, and opposite sides are equal. BC = 7 cm.
6. ABCD is a rectangle. Find ∠CAD.1 mark
Answer: 55°∠BAD is a right angle, 90°. ∠CAD = 90° − 35° = 55°.
7. ABCD is a rectangle. Name the side that is parallel to AD and a side that is perpendicular to AD.1 mark
Answer: Parallel: BC. Perpendicular: AB (or DC).Opposite sides are parallel, so BC is parallel to AD. Neighbouring sides meet at a right angle, so AB (or DC) is perpendicular to AD.
8. Each square is 1 cm by 1 cm. EFGH is a rectangle. What are the lengths of GH and FG?1 mark
Answer: GH = 7 cm, FG = 3 cmCount the squares. EF is 7 squares long, so GH = 7 cm. FG is 3 squares long, so FG = 3 cm.
9. How many pairs of parallel sides does a rectangle have?1 mark
Answer: 2 pairsThe two long sides are parallel, and the two short sides are parallel. That makes 2 pairs.
10. ABCD is a rectangle. Find its perimeter.2 marks
Answer: 38 cmOpposite sides are equal. 13 + 6 + 13 + 6 = 38 cm.
11. Each square is 1 cm by 1 cm. A, B and C are three corners of rectangle ABCD. Mark D and draw the rectangle. What is the length of AD?2 marks
Answer: AD = 3 cmD is 3 squares below A. AD is opposite BC, and BC is 3 cm. So AD = 3 cm.
12. ABCD is a rectangle. ∠BAC is 2 times as big as ∠CAD. Find ∠CAD.2 marks
Answer: 30°∠BAD = 90°. ∠BAC and ∠CAD make 3 equal parts, so 90° ÷ 3 = 30°. ∠CAD = 30°.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 8 · Answers and explanations
Lesson 8.3: Properties of Squares (answers)
Section A · Multiple choice 4 marks
1. How many equal sides does a square have?1 mark
(A) 4(B) 1(C) 2(D) 3
Answer: (A) 4All 4 sides of a square are equal in length.
2. Each small square is 1 cm by 1 cm. Which shape is a square?1 mark
(A) A(B) B(C) C(D) D
Answer: (B) BB is 3 squares by 3 squares, so all its sides are equal. A, C and D have sides of two different lengths.
3. Which statement is true?1 mark
(A) A square is not a rectangle.(B) A rectangle always has 4 equal sides.(C) A square is a special rectangle.(D) A square has only 2 right angles.
Answer: (C) A square is a special rectangle.A square has 4 right angles, like a rectangle, and its 4 sides are equal too. So a square is a special kind of rectangle.
4. PQRS is a square. What is the length of QR?1 mark
(A) 3 cm(B) 12 cm(C) 24 cm(D) 6 cm
Answer: (D) 6 cmAll sides of a square are equal. QR = PQ = 6 cm.
Section B · Write your answer 11 marks
5. ABCD is a square. Find its perimeter.1 mark
Answer: 28 cmAll 4 sides are 7 cm. 4 × 7 = 28 cm.
6. ABCD is a square. Name the sides that are perpendicular to AB.1 mark
Answer: AD and BCNeighbouring sides of a square meet at a right angle. AD and BC meet AB at its two ends, so they are perpendicular to AB.
7. Each square is 1 cm by 1 cm. A, B and C are three corners of a square ABCD. Mark D on the grid.1 mark
Answer: D is the empty corner, 3 squares from A and 3 squares from C.AB and BC are both 3 cm. The fourth corner D is 3 squares from A and 3 squares from C, so ABCD has 4 equal sides and 4 right angles.
8. Is this true or false? "Every rectangle is a square." Explain.1 mark
Answer: False. A rectangle can have sides of two different lengths.A square has 4 equal sides but a rectangle only needs opposite sides equal. For example, a rectangle 5 cm by 3 cm is not a square.
9. A square has a perimeter of 36 cm. What is the length of one side?1 mark
Answer: 9 cmThe 4 sides are equal. 36 ÷ 4 = 9 cm.
10. Each square is 1 cm by 1 cm. Which shapes are squares? Which shapes are rectangles but not squares?2 marks
Answer: Squares: A and C. Rectangles that are not squares: B and D.A is 3 by 3 and C is 2 by 2, so their sides are equal. B is 5 by 2 and D is 4 by 3, so their sides are not all equal.
11. Each square is 1 cm by 1 cm. A, B and C are three corners of a square ABCD. Mark D and draw the square. What is its perimeter?2 marks
Answer: 16 cmD is 4 squares above A. Each side is 4 cm. Perimeter = 4 × 4 = 16 cm.
12. Two squares with sides of 4 cm are put side by side to make a rectangle. What is the perimeter of the rectangle?2 marks
Answer: 24 cmThe rectangle is 8 cm long and 4 cm wide. 8 + 4 + 8 + 4 = 24 cm.
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Primary 4 Mathematics · Chapter 8 · Answers and explanations
Lesson 8.4: Drawing Squares and Rectangles (answers)
Section A · Multiple choice 4 marks
1. Which tool do you use to draw a right angle?1 mark
(A) ruler(B) set square(C) compass(D) eraser
Answer: (B) set squareA set square has a right-angle corner. A ruler only measures length and draws straight lines.
2. You want to draw a rectangle 6 cm by 3 cm. What should you do first?1 mark
(A) Draw the last side to close the shape.(B) Draw a line 3 cm long at a slant.(C) Draw a line 6 cm long with a ruler.(D) Join two corners together.
Answer: (C) Draw a line 6 cm long with a ruler.Start with one side. Draw a 6 cm line with a ruler, then use a set square to draw the sides at right angles.
3. You have drawn side AB. The next side BC of the rectangle must be ___ to AB.1 mark
Answer: (D) perpendicularIn a rectangle, neighbouring sides meet at a right angle. So BC must be perpendicular to AB.
4. Which is true for both a square and a rectangle (that is not a square)?1 mark
(A) They have 4 right angles.(B) They have 4 equal sides.(C) They have sides of two different lengths.(D) They have no parallel sides.
Answer: (A) They have 4 right angles.Squares and rectangles both have 4 right angles and 2 pairs of parallel sides. Only a square has 4 equal sides.
Section B · Write your answer 11 marks
5. Each square is 1 cm by 1 cm. K, L and M are three corners of rectangle KLMN. Mark N and draw the rectangle.1 mark
Answer: N is the empty corner, 5 squares to the right of M.N is the empty corner. KN is parallel and equal to LM, and MN is parallel and equal to LK.
6. Put these steps for drawing a rectangle in the right order. P: Join D and C. Q: Draw AB = 6 cm. R: At B, draw BC = 3 cm at a right angle to AB. S: At A, draw AD = 3 cm at a right angle to AB.1 mark
Answer: Q, S, R, P (Q, R, S, P is also correct)Draw one side first (Q). Then draw the two sides at right angles to it (S and R). Last, join the ends (P).
7. Write one way a square is different from a rectangle that is not a square.1 mark
Answer: All 4 sides of a square are equal. (A rectangle has sides of two different lengths.)Both shapes have 4 right angles. Only the square has all 4 sides equal.
8. Zara tried to draw a rectangle ABCD on the grid. What is wrong with her drawing?1 mark
Answer: AD is not at a right angle to AB, and DC is shorter than AB.D is in the wrong place. AD is slanted, so the angle at A is not a right angle. DC is 4 squares but AB is 5 squares, yet opposite sides of a rectangle must be equal.
9. Ali draws rectangle ABCD with AB = 9 cm and BC = 4 cm. What should the length of DC be?1 mark
Answer: 9 cmDC is opposite AB. Opposite sides of a rectangle are equal, so DC = 9 cm.
10. Each square is 1 cm by 1 cm. Draw a square ABCD below AB, using AB as one side. What is the length of each side?2 marks
Answer: 4 cmAB is 4 squares long. Draw AD and BC downward at right angles, each 4 cm. Join D and C. A square has 4 equal sides.
11. Each square is 1 cm by 1 cm. A and C are opposite corners of rectangle ABCD. The sides run along the grid lines. Draw the rectangle. What are its length and breadth?2 marks
Answer: Length 6 cm, breadth 3 cmFrom A go 6 squares across and from C go 3 squares up to find B. D is 3 squares below A. Join A, B, C and D.
12. Each square is 1 cm by 1 cm. Use a ruler and set square to draw a rectangle 7 cm long and 4 cm wide on the grid.2 marks
Answer: A rectangle 7 squares by 4 squares with 4 right angles (any position).Draw a 7 cm side, then draw 4 cm sides at right angles at both ends, then join the ends. Check that opposite sides are equal.
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Primary 4 Mathematics · Chapter 8 · Answers and explanations
Chapter 8 Revision Paper: Rectangles and Squares (answers)
Section A · Multiple choice 10 marks
1. Which line is perpendicular to AB?1 mark
(A) EF(B) CD(C) GH(D) none of them
Answer: (B) CDCD meets AB at a right angle. EF never meets AB, so it is parallel to AB. GH crosses AB at a slant, so it is not perpendicular.
2. Which statement about parallel lines is true?1 mark
(A) They must be the same length.(B) They meet at a right angle.(C) They never meet, however far they are extended.(D) They always meet at one point.
Answer: (C) They never meet, however far they are extended.Parallel lines stay the same distance apart and never meet. Their lengths do not matter. Lines that meet at a right angle are perpendicular.
3. Which kind of line is perpendicular to a vertical line?1 mark
(A) a vertical line(B) a slanted line(C) a line that never meets it(D) a horizontal line
Answer: (D) a horizontal lineA horizontal line meets a vertical line at a right angle, so it is perpendicular to it. A vertical line is parallel to it.
4. PQRS is a rectangle. What is the length of SR?1 mark
(A) 12 cm(B) 5 cm(C) 17 cm(D) 34 cm
Answer: (A) 12 cmOpposite sides of a rectangle are equal. SR is opposite PQ, so SR = 12 cm.
5. PQRS is a rectangle. Which sides are perpendicular to PQ?1 mark
(A) SR only(B) QR and PS(C) QR and SR(D) SR and PS
Answer: (B) QR and PSNeighbouring sides of a rectangle meet at right angles. The sides that meet PQ are QR and PS. SR is opposite PQ, so it is parallel to PQ, not perpendicular.
6. Each small square is 1 cm by 1 cm. Which shape is a rectangle that is NOT a square?1 mark
(A) B(B) C(C) A(D) D
Answer: (C) AA is 4 squares by 2 squares, so its sides are not all equal. B, C and D are 3 by 3, 2 by 2 and 4 by 4, so they are squares.
7. The perimeter of a square is 40 cm. What is the length of one side?1 mark
(A) 4 cm(B) 20 cm(C) 36 cm(D) 10 cm
Answer: (D) 10 cmA square has 4 equal sides. 40 ÷ 4 = 10 cm.
8. Which statement about a square is NOT true?1 mark
(A) Opposite sides are perpendicular.(B) All four sides are equal.(C) It has 4 right angles.(D) Opposite sides are parallel.
Answer: (A) Opposite sides are perpendicular.In a square the opposite sides are parallel, not perpendicular. The sides that meet at a corner are the perpendicular ones. All 4 sides are equal and all 4 angles are right angles.
9. Each small square is 1 cm by 1 cm. A, B and C are three corners of rectangle ABCD. Which point is corner D?1 mark
(A) W(B) X(C) Y(D) Z
Answer: (B) XD must be directly below A (same column) and directly left of C (same row), so ABCD has 4 right angles. Only point X is in the right place.
10. Ria is drawing a square of side 5 cm. She has drawn AB = 5 cm. What should she do next?1 mark
(A) Draw AD = 5 cm at any angle to AB.(B) Draw AD = 10 cm at a right angle to AB.(C) Draw AD = 5 cm at a right angle to AB.(D) Join A to the middle of AB.
Answer: (C) Draw AD = 5 cm at a right angle to AB.The sides of a square are equal, so AD = 5 cm. The sides meet at right angles, so use a set square to draw AD at a right angle to AB.
Section B · Short answers 4 marks
11. How many pairs of parallel lines are there in the figure?1 mark
Answer: 3 pairsAB, CD and EF are all straight across and never meet. AB // CD, AB // EF and CD // EF make 3 pairs. GH is perpendicular to each of them.
12. WXYZ is a rectangle. Find its perimeter.1 mark
Answer: 28 cmOpposite sides are equal. 9 + 5 + 9 + 5 = 28 cm.
13. Is a square also a rectangle? Write yes or no and give a reason.1 mark
Answer: Yes. A square has 4 right angles and its opposite sides are equal and parallel.A rectangle has 4 right angles with opposite sides equal and parallel. A square has all of these, so a square is a special rectangle.
14. Each square is 1 cm by 1 cm. A, B and C are three corners of square ABCD. Mark D on the grid.1 mark
Answer: D is the empty corner, 3 squares to the right of A and 3 squares above C.AB and BC are both 3 cm. D is 3 squares from A and 3 squares from C, so ABCD has 4 equal sides and 4 right angles.
Section C · Show your working 16 marks
15. (a) Name two lines that are perpendicular to PQ. (b) Name the line that is parallel to XY.2 marks
Answer: (a) RS and TU (b) PQ(a) RS and TU are straight up and down and meet PQ at right angles. VW is slanted, so it is not perpendicular. (b) PQ and XY are both straight across and never meet, so PQ is parallel to XY.
16. Use a set square and a ruler. (a) Draw a line from P to AB so that it is perpendicular to AB. (b) Draw a line through Q that is parallel to AB.2 marks
Answer: (a) Line from P straight down to AB, meeting it at a right angle. (b) Line through Q straight across, never meeting AB.(a) Put the set square on AB with its right-angle corner on the line, slide it until its edge touches P, then draw. (b) Draw along the grid line through Q. It stays the same distance from AB, so it is parallel.
17. ABCD is a rectangle. BC = 6 cm. The perimeter of the rectangle is 40 cm. Find the length of AB.2 marks
Answer: 14 cmHalf of the perimeter is AB + BC: 40 ÷ 2 = 20 cm. AB = 20 − 6 = 14 cm.
18. ABCD is a rectangle. ∠BAC = 30°. (a) Find ∠CAD. (b) How many degrees bigger is ∠CAD than ∠BAC?2 marks
Answer: (a) 60° (b) 30°(a) ∠BAD is a right angle, 90°. ∠CAD = 90° − 30° = 60°. (b) 60° − 30° = 30°.
19. Three squares with sides of 5 cm are put in a row to make a rectangle. Find the perimeter of the rectangle.2 marks
Answer: 40 cmThe rectangle is 3 × 5 = 15 cm long and 5 cm wide. 15 + 5 + 15 + 5 = 40 cm.
20. A square has the same perimeter as a rectangle that is 14 cm long and 10 cm wide. Find the length of one side of the square.2 marks
Answer: 12 cmPerimeter of the rectangle = 14 + 10 + 14 + 10 = 48 cm. The square has 4 equal sides, so one side is 48 ÷ 4 = 12 cm.
21. Each square is 1 cm by 1 cm. K, L and M are three corners of rectangle KLMN. Mark N and draw the rectangle. What is its perimeter?2 marks
Answer: 18 cmN is 6 squares to the right of K and 3 squares above M. The rectangle is 6 cm long and 3 cm wide. 6 + 3 + 6 + 3 = 18 cm.
22. The length of rectangle ABCD is 3 times its breadth. Its perimeter is 48 cm. (a) Find the breadth. (b) A square has sides equal to the breadth of the rectangle. Find the perimeter of the square.2 marks
Answer: (a) 6 cm (b) 24 cm(a) The perimeter is 3 + 1 + 3 + 1 = 8 units of the breadth. 48 ÷ 8 = 6, so the breadth is 6 cm. (b) The square has sides of 6 cm. 4 × 6 = 24 cm.
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