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
ASA
The correct answer is ASA.
To determine which theorem or postulate can be used to prove triangle ABE congruent to triangle CDE, we need to analyze the information derived from questions 2, 3, and 4.
Question 2 states that triangle ABD is congruent to triangle CDB. This means that they have the same shape and size.
Question 3 mentions that the figure shown is a parallelogram, with points A, B, C, and D arranged in a clockwise fashion.
Question 4 describes that the two diagonal lines from points A to C and from points B to D intersect at point E.
Based on this information, the theorem or postulate that can be used to prove triangle ABE congruent to triangle CDE is the ASA (Angle-Side-Angle) congruence postulate. This postulate 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 two triangles are congruent.
In this case, we can observe that angle ABE is congruent to angle CDE (due to the intersection of the diagonal lines), angle AEB is congruent to angle CDE (alternate interior angles formed by parallel lines), and we know that side BE is congruent to side DE (due to the congruent triangles ABD and CDB).
Therefore, by using the ASA postulate, we can prove that triangle ABE is congruent to triangle CDE.