Question

Danny analyzes the given triangles below. He determines that sides de-ba. He also determines that angle a and angle e are congruent. He then concludes that the triangles are congruent by the SAS congruence theorem. What is the reason Danny used to conclude that the triangles are congruent?

1) SSS congruence theorem
2) ASA congruence theorem
3) SAS congruence theorem
4) AAS congruence theorem

Answer 1

Danny concluded that the triangles are congruent using the SAS congruence theorem because he identified two pairs of congruent sides with a congruent angle between them.

Step-by-step explanation:

Danny used the SAS congruence theorem to conclude that the triangles are congruent because he has identified two pairs of corresponding sides that are of equal length and the angle between these sides is also congruent in both triangles. The Side-Angle-Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Danny cannot use the SSS, ASA, or AAS congruence theorems since he has not mentioned three sides, two angles and the included side, or two angles and the non-included side being congruent, respectively.