Question

Are the triangles similar, if so why? What would be the correct similarity statement if similar? The triangles _____ similar. The reason they are similar is _____ The similarity statement would be _____
(GHS Triangle. HS is 24, SG is 14. RQS Triangle. QS is 84, SR is 49)
(Options to use for the first blank is aren't, are. Options for the second blank is AA, SSS, aren't similar, SAS. Options for the last blank is GHS~RQS, aren't similar, GHS~QRS, GHS~QSR)

Answer 1

To determine if the triangles GHS and RQS are similar, we can compare the ratios of the lengths of their corresponding sides.

For triangle GHS:
- HS = 24
- SG = 14

For triangle RQS:
- QS = 84
- SR = 49

Let's first check the ratios of the corresponding sides:

1. Ratio of side HS to side QS:
\[
\frac{HS}{QS} = \frac{24}{84} = \frac{2}{7}
\]

2. Ratio of side SG to side SR:
\[
\frac{SG}{SR} = \frac{14}{49} = \frac{2}{7}
\]

Since both ratios \( \frac{HS}{QS} \) and \( \frac{SG}{SR} \) are equal (\( \frac{2}{7} \)), we can conclude that the triangles are similar by the Side-Side-Side (SSS) similarity criterion.

The correct similarity statement is as follows:
- The triangles **are similar**.
- The reason they are similar is **SSS** (since the ratio of the lengths of the corresponding sides are equal).
- The similarity statement would be **GHS~RQS**.

Therefore, the final answer is:

The triangles **are** similar. The reason they are similar is **SSS**. The similarity statement would be **GHS~RQS**.