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Similar Triangles

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

'Similar Triangles' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Pythagoras' Theorem and Trigonometric Ratios to Find Angles and Lengths in 2D Figures

Difficulty level:  

down

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

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

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

 

 

(not drawn to scale)

  • Question 1

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

 

 

(not drawn to scale)

CORRECT ANSWER
9.8
EDDIE SAYS
Scale factor = 7 ÷ 5 = 1.4
x = 1.4 × 7 = 9.8
  • Question 2

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

 

 

(not drawn to scale)

CORRECT ANSWER
4
EDDIE SAYS
Scale factor = 7 ÷ 5 = 1.4
y = 5.6 ÷ 1.4 = 4
  • Question 3

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

 

 

(not drawn to scale)

CORRECT ANSWER
5.6
EDDIE SAYS
Scale factor = 8 ÷ 5 = 1.6
x = 3.5 × 1.6 = 5.6
  • Question 4

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

 

 

(not drawn to scale)

CORRECT ANSWER
4.375
EDDIE SAYS
Scale factor = 8 ÷ 5 = 1.6
y = 7 ÷ 1.6 = 4.375
  • Question 5

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

 

 

(not drawn to scale)

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.

 

 

(not drawn to scale)

CORRECT ANSWER
6
EDDIE SAYS
Scale factor = 24.5 ÷ 7 = 3.5
y = 21 ÷ 3.5 = 6
  • Question 7

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

 

 

(not drawn to scale)

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.

 

 

(not drawn to scale)

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.

 

 

(not drawn to scale)

CORRECT ANSWER
48.75
EDDIE SAYS
Scale factor = 45.5 ÷ 14 = 3.25
x = 15 × 3.25 = 48.75
  • Question 10

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

 

 

(not drawn to scale)

CORRECT ANSWER
8.2
EDDIE SAYS
Scale factor = 45.5 ÷ 14 = 3.25
y = 33.6 ÷ 3.25 = 8.2
---- OR ----

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