Similarity of Perimeters in Triangles

Similarity of Perimeters in Triangles

How to solve the similarity of perimeters in triangles problems: example and its solution.

Example

Find the perimeter of triangle A'B'C'. The measures of sides of triangle ABC: 6, 7, and 8. The measure of the side of triangle A'B'C': 9.

These two triangles have two pairs of congruent angles.

So, by the AA similarity,
these two triangles are similar.

If two triangles are similar,
then their perimeters are proportional.

So, find P to use it:
P = 7 + 8 + 9 = 21.

The perimeters and the sides are proportional.
So P / P' = 6 / 9.

Put 21 into the proportion:
21 / P' = 6 / 9.