Shape and space · Ages 7–8
Right angles and perpendicular lines worksheet
Part of: Solids, angles and quadrilaterals
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Right angles and perpendicular lines worksheet
Shape and space · Ages 7–8
Numsprite
numsprite.com
Name:Date:Score:／46
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.How many pairs of neighbouring sides of this shape are perpendicular?
Answer:
Part B: Choose, or true or false (2 marks each)
2.Which pair of lines is perpendicular?
- A
- B
- C
- D
Choose the right picture
Answer:
3.The two lines in the picture are perpendicular.
True or false?
Answer:
4.Four segments run from point P to the line. Which is the shortest?
- A. PB
- B. PA
- C. PD
- D. PC
Choose the right answer
Answer:
5.The perpendicular segment from point P to a line is 9 cm. Which could be the length of a segment from P to another point on the line?
- A. 7 cm
- B. 8 cm
- C. 13 cm
- D. 6 cm
Choose the right answer
Answer:
6.The perpendicular segment from point P to a line is 11 cm. Which could be the length of a segment from P to another point on the line?
- A. 16 cm
- B. 8 cm
- C. 9 cm
- D. 10 cm
Choose the right answer
Answer:
7.The perpendicular segment from point P to a line is 6 cm. Which could be the length of a segment from P to another point on the line?
- A. 3 cm
- B. 4 cm
- C. 5 cm
- D. 10 cm
Choose the right answer
Answer:
8.The perpendicular segment from point P to a line is 7 cm. Which could be the length of a segment from P to another point on the line?
- A. 13 cm
- B. 6 cm
- C. 4 cm
- D. 5 cm
Choose the right answer
Answer:
9.The perpendicular segment from point P to a line is 8 cm. Which could be the length of a segment from P to another point on the line?
- A. 5 cm
- B. 7 cm
- C. 6 cm
- D. 11 cm
Choose the right answer
Answer:
10.The perpendicular segment from point P to a line is 12 cm. Which could be the length of a segment from P to another point on the line?
- A. 16 cm
- B. 10 cm
- C. 11 cm
- D. 9 cm
Choose the right answer
Answer:
11.The perpendicular segment from point P to a line is 10 cm. Which could be the length of a segment from P to another point on the line?
- A. 8 cm
- B. 7 cm
- C. 9 cm
- D. 13 cm
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
12.The shortest distance from P to the riverbank is 28 m. Ka-lok walks from P to the bank at a slant and covers 26 m. This could happen.
True or false?
Working:
Answer:
13.At a crossroads two perpendicular roads meet, making 4 right angles. How many right angles do 5 such crossroads make?
Working:
Answer:
14.Chi-keung stands at P and wants to reach the straight road ahead (see the picture). Which way is shortest?
- A. PA
- B. PD
- C. PC
- D. PB
Choose the right answer
Working:
Answer:
15.The shortest distance from P to the riverbank is 42 m. Ming walks from P to the bank at a slant and covers 37 m. This could happen.
True or false?
Working:
Answer:
16.Tsz-ching stands at P and wants to reach the straight road ahead (see the picture). Which way is shortest?
- A. PD
- B. PC
- C. PA
- D. PB
Choose the right answer
Working:
Answer:
17.At a crossroads two perpendicular roads meet, making 4 right angles. How many right angles do 4 such crossroads make?
Working:
Answer:
Show the answers and working
Right angles and perpendicular lines worksheet: Answers and working
Part A: Working out and filling in
1. 4 pairs
Neighbouring sides that are perpendicular make a right angle where they meet. Check each corner with a set square.
Perpendicular neighbours make a right angle where they meet: count the right angles, 4.
Part B: Choose, or true or false
2. D
Perpendicular lines cross at a right angle. Check where each pair crosses with a set square.
Perpendicular lines cross at right angles: all four angles are equal.
3. False
Hold a set square where the lines cross: is the angle a right angle?
Check the angle where they cross with a set square: only a right angle means perpendicular.
4. C. PD
Of the segments from P to the line, which meets it at a right angle? The slanting ones are longer.
The segment perpendicular to the line is the shortest.
5. C. 13 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 9 cm?
The perpendicular is shortest; any other segment is longer than 9 cm.
6. A. 16 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 11 cm?
The perpendicular is shortest; any other segment is longer than 11 cm.
7. D. 10 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 6 cm?
The perpendicular is shortest; any other segment is longer than 6 cm.
8. A. 13 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 7 cm?
The perpendicular is shortest; any other segment is longer than 7 cm.
9. D. 11 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 8 cm?
The perpendicular is shortest; any other segment is longer than 8 cm.
10. A. 16 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 12 cm?
The perpendicular is shortest; any other segment is longer than 12 cm.
11. D. 13 cm
The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 10 cm?
The perpendicular is shortest; any other segment is longer than 10 cm.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
12. False
The shortest way is the perpendicular 28 m. Is a slanting walk longer or shorter than that? Compare with 26.
The shortest is the perpendicular 28 m; a slanting walk is always further.
13. 20 right angles
Each crossroads has 4 right angles, so 5 of them are 5 lots of 4.
4 each, so 5 make 20.
14. C. PC
Of the ways from P to the road, which meets the road at a right angle? The slanting ones are longer.
The way perpendicular to the road is shortest.
15. False
The shortest way is the perpendicular 42 m. Is a slanting walk longer or shorter than that? Compare with 37.
The shortest is the perpendicular 42 m; a slanting walk is always further.
16. C. PA
Of the ways from P to the road, which meets the road at a right angle? The slanting ones are longer.
The way perpendicular to the road is shortest.
17. 16 right angles
Each crossroads has 4 right angles, so 4 of them are 4 lots of 4.
4 each, so 4 make 16.
Numsprite · numsprite.com/en/worksheets/solids-angles-and-quadrilaterals/perpendicular-lines
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