Question

consider the two triangles. to prove that the triangles are similar by the sas similarity theorem, it needs to be shown that

∠c≅∠c
∠c≅∠g
\frac{ac}{gi}=\frac{hi}{bc}
\frac{ac}{gi}=\frac{bc}{hi}

15
20
9
12
a
b
c
h
i
g

Explanation:

Step1: Recall SAS similarity theorem

SAS (Side - Angle - Side) similarity requires the ratio of two pairs of corresponding sides to be equal and the included angles to be congruent.

Step2: Identify corresponding sides

Corresponding sides of \(\triangle ABC\) and \(\triangle HIG\) should be in proportion. The correct proportion for the sides is \(\frac{AC}{GI}=\frac{BC}{HI}\).

Answer:

D. \(\frac{AC}{GI}=\frac{BC}{HI}\)