# Identify Similar Triangles and Parallel Lines

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

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Draw and Measure Line Segments and Angles

Difficulty level:

### QUESTION 1 of 10

Triangles which have exactly the same angles are similar.

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

We can find similar triangles when a triangle is cut by a line parallel to the base as in the example below:

This is because the apex (top) angle is in both triangle ABC and in triangle ADE.

∠ABC = ∠ADE because they are corresponding angles on parallel lines.

The third angles automatically match and therefore the triangles are similar.

Separate the triangles to make the similar proportions easier to spot.

Triangle ABC is similar to Triangle ADE.

Example:

Find the value of y from the information given in this diagram.

(Not to scale.)

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

Comparing corresponding sides, we get that the scale factor is 5.85 ÷ 4.5 = 1.3

y = 1.3 × 5 = 6.5

Now, let's tackle some questions together!

Find the value of x from the information given in this diagram.

(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 this diagram.

(Not drawn to scale.)

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

48

66.42

8.2

4.1

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

• Question 1

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

10
EDDIE SAYS
Comparing corresponding sides, we can calculate that the scale factor is 9 ÷ 4.5 = 2. x = 2 × 5 = 10 How did you get on?
• Question 2

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

(Not drawn to scale.)

10.5
EDDIE SAYS
Comparing corresponding sides, we can identify that the scale factor is 9 ÷ 6 = 1.5 x = 7 × 1.5 = 10.5 Once you calculate scale, these questions are pretty straight-forward.
• Question 3

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

8
EDDIE SAYS
By comparing corresponding sides, we can identify that the scale factor is 9 ÷ 6 = 1.5 Therefore, y = 12/1.5 = 8 If you're still struggling, you can always turn back to the introduction in order to re-read the explanation.
• Question 4

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

9.6
EDDIE SAYS
First, we calculate scale factor = 7.5 ÷ 6 = 1.25 Then we apply this scale to find y = 12 ÷ 1.25 = 9.6 This should be starting to feel like second nature by this point, the calculation stays the same each time. It's the scale that changes and has to be substituted in.
• Question 5

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

9.45
EDDIE SAYS
Scale factor = 8.1 ÷ 6 = 1.35 x = 7 × 1.35 = 9.45 How are you finding these?
• Question 6

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

8.2
EDDIE SAYS
Scale factor = 8.1 ÷ 6 = 1.35 So, y = 11.07 ÷ 1.35 = 8.2
• Question 7

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

7.2
EDDIE SAYS
Scale factor = 7.83 ÷ 5.4 = 1.45 Therefore, y = 10.44 ÷ 1.45 = 7.2
• Question 8

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

11.658
EDDIE SAYS
Scale factor = 7.83 ÷ 5.4 = 1.45 x = 8.04 × 1.45 = 11.658
• Question 9

Find the value of x from the information given in this diagram.

(Not drawn to scale.)

12
EDDIE SAYS
Scale factor = (6 + 3) ÷ 6 = 1.5 x = 8 × 1.5 = 12
• Question 10

Find the value of y from the information given in this diagram.

(Not drawn to scale.)

7.4
EDDIE SAYS
Scale factor = (5 + 4) ÷ 5 = 1.8 y = 13.32 ÷ 1.8 = 7.4 Phew, that was a challenge but you got through the activity! Great focus, now take a well-deserved break.
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