Question

The triangles below are similar.

Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters.

Which similarity statement expresses the relationship between the two triangles?
Triangle Z Y X is similar to triangle C A B
Triangle Z Y X is similar to triangle A C B
Triangle Z Y X is similar to triangle C B A
Triangle Z Y X is similar to triangle A B C

Answer 1

To determine the similarity statement between triangles YXZ and ABC, we need to compare the lengths of their corresponding sides.

For triangle YXZ:
- Side YX = 6 cm
- Side XZ = 7 cm
- Side ZY = 3 cm

For triangle ABC:
- Side AC = 14 cm
- Side AB = 12 cm
- Side BC = 6 cm

Next, we will find the ratios of the corresponding sides from the two triangles:

1. To find the ratio of side YX to side AB:
\[
\frac{YX}{AB} = \frac{6}{12} = \frac{1}{2}
\]

2. To find the ratio of side XZ to side AC:
\[
\frac{XZ}{AC} = \frac{7}{14} = \frac{1}{2}
\]

3. To find the ratio of side ZY to side BC:
\[
\frac{ZY}{BC} = \frac{3}{6} = \frac{1}{2}
\]

Since all three ratios are equal (1/2), the triangles are indeed similar.

Now, we need to match the vertices of triangles YXZ and ABC:

- Y corresponds to C
- X corresponds to A
- Z corresponds to B

This leads us to the similarity statement:

**Triangle ZYX is similar to triangle CAB.**

Therefore, the correct choice is:
- Triangle Z Y X is similar to triangle C A B.