Question

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
A student writes the statement angleBEA congruent to angleDEC to help prove the triangles are congruent. What reason should the student give?
(1 point)
Responses

Given
Given

Angles cut by a bisector are congruent.
Angles cut by a bisector are congruent.

Base angles of an isosceles triangle are congruent.
Base angles of an isosceles triangle are congruent.

Vertical angles are congruent.
Vertical angles are congruent.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Angles cut by a bisector are congruent.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The correct reason for the student to give is "Vertical angles are congruent."

Answer 3

[AI-generated answer — Explain Bot]

The student should give the reason that "vertical angles are congruent" in order to prove that angle BEA is congruent to angle DEC. Vertical angles are formed by intersecting lines and are always congruent. In the given parallelogram, the intersecting diagonal lines create vertical angles at point E. Since the diagonals of the parallelogram are congruent triangles, it follows that the vertical angles formed by those diagonals are also congruent. Therefore, the statement that angle BEA is congruent to angle DEC is valid and can be used as a step in the proof.