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
Which of the following sets of angles are congruent by the Alternate Interior Angles Theorem?
(1 point)
Responses

angleA congruent to angleC
Image with alt text: angle A Image with alt text: congruent to Image with alt text: angle C

angleCDE congruent to angleABE
Image with alt text: angle CDE Image with alt text: congruent to Image with alt text: angle ABE

angleAED congruent toangleCEB
Image with alt text: angle AED Image with alt text: congruent to Image with alt text: angle CEB

angleBAC congruent toangleCDB

Answer 1

[AI-generated answer — Bot GPT 3.5]

Based on the given information, the angles that are congruent by the Alternate Interior Angles Theorem are:

angle A congruent to angle C

Therefore, the correct answer is:

angle A congruent to angle C

Answer 2

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

According to the given information, the angles that are congruent by the Alternate Interior Angles Theorem are:

- angle A is congruent to angle C

Answer 3

[AI-generated answer — Explain Bot]

To determine which sets of angles are congruent by the Alternate Interior Angles Theorem, you need to understand what the theorem states. The Alternate Interior Angles Theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.

In the given information, it is mentioned that line AB is parallel to line CD since it is a parallelogram. The intersection point of the diagonals is marked as point E. Therefore, the transversal is the line passing through points A, E, and C.

Now, let's analyze each set of angles mentioned in the question:

1. angle A congruent to angle C:
This set of angles does not meet the condition of the Alternate Interior Angles Theorem because angle A and angle C are not alternate interior angles. They are corresponding angles.

2. angle CDE congruent to angle ABE:
This set of angles meets the condition of the Alternate Interior Angles Theorem because angle CDE and angle ABE are alternate interior angles formed by the transversal line and the parallel lines AB and CD.

3. angle AED congruent to angle CEB:
This set of angles does not meet the condition of the Alternate Interior Angles Theorem because angle AED and angle CEB are not alternate interior angles. They are vertical angles.

4. angle BAC congruent to angle CDB:
This set of angles does not meet the condition of the Alternate Interior Angles Theorem because angle BAC and angle CDB are not alternate interior angles. They are corresponding angles.

Based on the analysis, the set of angles that are congruent by the Alternate Interior Angles Theorem is:
angle CDE congruent to angle ABE.