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Revise Similar Triangles

In this worksheet, students will revise similar triangles and use proportions to work out the lengths of sides.

'Revise Similar Triangles' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Problems Involving Perimeters and Areas of 2D Shapes

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Triangles which have exactly the same angles are similar.

If two angles match, the third angle will automatically match as the angle sum is always 180º.

 

Similar triangles have corresponding sides which are in the same ratio or proportion.

 

 

Here, the lengths of the sides in the right hand triangle are 1.5 times the lengths of the matching sides in the left hand triangle.

 

Example

Find the value of x from the information given in these triangles.

 

 

Answer

The triangles are similar because two angles match, and so will the third too.

Comparing corresponding sides, we get that the scale factor is 7 ÷ 5 = 1.4

x = 1.4 × 6 = 8.4

 

Now it's over to you!

Find the value of x from the information given in these triangles.

 

 

 

 

Find the value of y from the information given in these triangles.

 

 

 

 

Find the value of x from the information given in these triangles.

 

 

 

 

Find the value of y from the information given in these triangles.

 

 

 

 

4.375

11.2

0.714

1.6

Find the value of x from the information given in these triangles.

 

 

 

 

Find the value of y from the information given in these triangles.

 

 

 

 

Find the value of x from the information given in these triangles.

 

 

 

 

Find the value of y from the information given in these triangles.

 

 

 

Find the value of x from the information given in these triangles.

 

 

 

 

Find the value of y from the information given in these triangles.

 

 

 

 

  • Question 1

Find the value of x from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
9.8
EDDIE SAYS
Scale factor = 7 ÷ 5 = 1.4 Therefore, x = 1.4 × 7 = 9.8 Strong start! Hopefully you worked out how to calculate the scale factor to then find x.
  • Question 2

Find the value of y from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
4
EDDIE SAYS
Scale factor = 7 ÷ 5 = 1.4 y = 5.6 ÷ 1.4 = 4 Was this question easier or more difficult? Remember you can always turn back to the introduction if you're struggling.
  • Question 3

Find the value of x from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
5.6
EDDIE SAYS
Scale factor = 8 ÷ 5 = 1.6 (you can identify the correlating sides by first recognising the correlating angles, as shown with the red lines). x = 3.5 × 1.6 = 5.6
  • Question 4

Find the value of y from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
4.375
EDDIE SAYS
Scale factor = 8 ÷ 5 = 1.6 y = 7 ÷ 1.6 = 4.375 You're make giant strides in your progress, push on!
  • Question 5

Find the value of x from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
12.25
EDDIE SAYS
Scale factor = 24.5 ÷ 7 = 3.5 x = 3.5 × 3.5 = 12.25
  • Question 6

Find the value of y from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
6
EDDIE SAYS
Scale factor = 24.5 ÷ 7 = 3.5 y = 21 ÷ 3.5 = 6 Take a deep breath, you've got this.
  • Question 7

Find the value of x from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
63
EDDIE SAYS
Scale factor = 71.4 ÷ 17 = 4.2 x = 15 × 4.2 = 63
  • Question 8

Find the value of y from the information given in these triangles.

 

 

 

CORRECT ANSWER
8
EDDIE SAYS
Scale factor = 71.4 ÷ 17 = 4.2 y = 33.6 ÷ 4.2 = 8
  • Question 9

Find the value of x from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
48.75
EDDIE SAYS
Scale factor = 45.5 ÷ 14 = 3.25 x = 15 × 3.25 = 48.75 One more question to go!
  • Question 10

Find the value of y from the information given in these triangles.

 

 

 

 

CORRECT ANSWER
8.2
EDDIE SAYS
Scale factor = 45.5 ÷ 14 = 3.25 y = 33.6 ÷ 3.25 = 8.2 Great work! That's another activity all ticked off. Why not attempt another one so that you feel super confident?
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