Question

cp geometry a o / congruence and similarity

1. which of the following additional statements would you need to prove these two triangles are similar by sas similarity?

∠g≅∠j
∠h≅∠k
∠i≅∠l
∠i≅∠k

Explanation:

Step1: Recall SAS similarity

SAS (Side - Angle - Side) similarity rule states that if the ratios of two pairs of corresponding sides of two triangles are equal and the included angles are congruent, the triangles are similar.
For \(\triangle GHI\) and \(\triangle JKL\), we have \(\frac{GI}{JL}=\frac{18}{27}=\frac{2}{3}\) and \(\frac{HI}{KL}=\frac{12}{18}=\frac{2}{3}\). The included angles for these sides are \(\angle I\) and \(\angle L\).

Step2: Determine the required angle

To prove similarity by SAS, we need the included angles to be congruent. So we need \(\angle I\cong\angle L\).

Answer:

\(\angle I\cong\angle L\)