Question

To prove that ΔAED ˜ ΔACB by SAS, Jose shows that StartFraction A E Over A C EndFraction = StartFraction A D Over A B EndFraction.

Triangle A E D is shown. Line segment B C is drawn from side A D to A E to form triangle A C B.

Jose also has to state that

Answer 1

Jose has established that two pairs of sides are proportional, but he must demonstrate that the included angle is congruent for SAS similarity of ΔAED and ΔACB.

Step-by-step explanation:

To prove that ΔAED is similar to ΔACB by the SAS (Side-Angle-Side) similarity criterion, Jose has correctly shown that AE/AC = AD/AB. However, to complete the proof using SAS, Jose must also show that there is an equivalence of angles between the two triangles. Specifically, Jose needs to demonstrate that ∠EAD is congruent to ∠CAB. The angle-angle (AA) condition is not enough for SAS similarity, as it would only prove the triangles are similar through AA, not SAS. By showing two sides are proportional and the included angle is congruent between the two triangles, SAS similarity will be established.