Triangles P and Q are similar. Find the lengths of the sides

Answers:

Explanation:

In triangle P, aka triangle ABC, we have the color coded angles:

For triangle Q, aka triangle XYZ, we have:

The colors must pair up to match together. The order is important. That order being "blue, purple, red".

Because of this, we have the three pairs of congruent angles:

Furthermore, that extends to having these pair of corresponding sides that match up together:

Side AC = 7 involves the blue and red angles. The same applies to XZ = 21.

The jump from 7 to 21 is "times 3", which tells us the scale factor. The triangle XYZ has side lengths 3 times longer compared to triangle ABC.

We'll use this scale factor to determine the missing sides of each triangle.

Side BC = 5 involves the purple and red angles. For the other triangle, side ZY involves those same color angles. Going from BC = 5 to ZY = unknown will involve the "times 3" operation. So we have,

ZY = 3*BC = 3*5 = 15

Side AB = unknown pairs up with side XY = 27 of the other triangle. Each side mentioned involves the blue and purple angles.

Instead of multiplying, we'll do the opposite: we divide 27 by 3 to get the side of AB.

This is because:

XY = 3*AB

AB = XY/3

AB = 27/3

AB = 9

figure c

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