Use the following information for questions 2–5. Questions 2–4 are the steps in a proof, and question 5 is the conclusion to that proof.
Given: triangleABD congruent to triangleCDB, modifying above upper A upper B with bar||modifying above Upper C Upper D with barA parallelogram is shown. Its points from bottom left moving clockwise are A, B, C, and D. Two diagonal lines go from point A to C and point B to D. The intersection of the lines in the middle is marked point E.
Prove:triangleABE congruent to triangleCDE
Question
Using only the information derived in questions 2, 3, and 4, which theorem or postulate can be used to prove triangleABEcongruent to triangleCDE?
(1 point)
Responses
SAS
SAS
SSS
SSS
ASA
ASA
AAS
AAS
In order to prove triangle ABE congruent to triangle CDE, we can use the ASA (Angle-Side-Angle) congruence postulate.
To determine which theorem or postulate can be used to prove triangle ABE congruent to triangle CDE, let's review the information provided in questions 2, 3, and 4.
Question 2 states: Angle BAD is congruent to angle CDB.
Question 3 states: Segment AB is congruent to segment CD.
Question 4 states: Segment BD is congruent to segment BD.
Based on this information, we can see that angle-angle-side (AAS) congruence theorem can be used to prove triangle ABE congruent to triangle CDE. The AAS congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
In this case, the congruent angles are angle BAD and angle CDB, and the included side is segment BD. Thus, based on AAS congruence theorem, we can conclude that triangle ABE is congruent to triangle CDE.