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
Image with alt text: angle BAC Image with alt text: congruent to Image with alt text: angle CDB
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The correct set of angles that are congruent by the Alternate Interior Angles Theorem is: angle BAC congruent to angle CDB.
The correct answer is: angleA congruent to angleC.
To determine which sets of angles are congruent by the Alternate Interior Angles Theorem, we need to consider the pairs of angles formed by the two intersecting lines (AC and BD) and the parallel lines (AB and CD).
The Alternate Interior Angles Theorem states that when a transversal crosses two parallel lines, the alternate interior angles formed are congruent.
In the given figure, the angles formed by the intersecting lines AC and BD are angle A and angle C. Therefore, angle A and angle C are congruent by the Alternate Interior Angles Theorem.
Thus, the correct answer is:
angle A congruent to angle C.