Question

to prove that ( \triangle aed sim \triangle acb ) by sas, jose shows that ( \frac{ae}{ac}=\frac{ad}{ab} ). jose also has to state that ( angle acongangle a ) ( angle acongangle d ) ( angle acongangle acb ) ( angle acongangle abc )

Explanation:

For the SAS (Side - Angle - Side) similarity criterion, we need two pairs of sides in proportion and the included angle equal. Here, \(\frac{AE}{AC}=\frac{AD}{AB}\) are the sides in proportion. The included angle for \(\triangle AED\) and \(\triangle ACB\) is \(\angle A\) which is common to both triangles. So, \(\angle A\cong\angle A\) (by the reflexive property of angles).

Answer:

\(\angle A\cong\angle A\) (i.e., the first option \(\angle A\cong\angle A\))