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Proportions 2

To review the basics of solving proportions, see here.

In this topic, you will apply proportions to similar figures. Similar figures have exactly the same shape but do not have the same size. This means that similar figures have the same angles and their sides are proportional.
The two triangles have the same angles.
The two triangles have proportional sides.
 = =
The side with length 8 and the side width length 16 are on the same side of the same angle on their respective triangles. This pair of sides are called corresponding sides. Corresponding sides are always proportional.

Example 1: Triangles

Find the value of 'n'.
 n =
The angles of the two triangles are the same so the sides of the triangles are proportional.

Step 1: Find the corresponding sides

 Top Triangle Bottom Triangle Corresponding Pair 1 7 56 Corresponding Pair 2 13 104 Corresponding Pair 3 n 80
The pairs of corresponding sides are related by
 = =
Step 2: Set up an equation with proportions using n and solve for n
Let us use the equation
 =
 Since = , the problem becomes =
When we cross multiply, it results in 1 × 80 = 8 × n

Now solve for n.
 1 × 80 = 8 × n (1 × 80) ÷ 8 = (8 × n) ÷ 8 10 = n

The answer is n:

Example 2: Trapezoids

Solve for n.
 n =
The angles of the two trapezoids are the same so the sides of the trapezoids are proportional.

Step 1: Find the corresponding sides

 Left Trapezoid Right Trapezoid Corresponding Pair 1 n 18 Corresponding Pair 2 19 57 Corresponding Pair 3 20 60 Corresponding Pair 4 22 66
The pairs of corresponding sides are related by
 = = =
Step 2: Set up an equation with proportions using n and solve for n
Let us use the equation
 =
 Since = , the problem becomes =
When we cross multiply, it results in n × 3 = 1 × 18

Now solve for n.
 n × 3 = 1 × 18 (n × 3) ÷ 3 = (1 × 18) ÷ 3 n = 6

The answer is n:

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