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.

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
Using the Given information above, which of the following statements can be proved by CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and is needed to work toward the prove statement?
(1 point)
Responses

angle Upper D Upper C Upper E approximately-equals angle Upper B Upper A Upper E
Image with alt text: angle Upper D Upper C Upper E approximately-equals angle Upper B Upper A Upper E

angle Upper B Upper A Upper D approximately-equals angle Upper D Upper C Upper B
Image with alt text: angle Upper B Upper A Upper D approximately-equals angle Upper D Upper C Upper B

Modifying over Upper A Upper D with bar approximately-equals Modifying over Upper C Upper B with bar
Image with alt text: Modifying over Upper A Upper D with bar approximately-equals Modifying over Upper C Upper B with bar

Modifying over Upper A Upper B with bar approximately-equals Modifying over Upper C Upper D with bar

Answer 1

Image with alt text: Modifying over Upper A Upper B with bar approximately-equals Modifying over Upper C Upper D with bar

Answer 2

Using the Given information above, the statement that can be proved by CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and is needed to work toward the prove statement is:

Modifying over AB with bar approximately-equals Modifying over CD with bar

Answer 3

To determine which statement can be proved by CPCTC and is needed to work toward the prove statement, we need to look for pairs of corresponding parts (sides or angles) that are congruent in the given information.

In this case, we are given that triangle ABD is congruent to triangle CDB. From the given information, we can see that angle A is corresponding to angle C and angle B is corresponding to angle D.

Therefore, the statement that can be proved by CPCTC and is needed to work toward the prove statement is:

angle DCE ≅ angle BAE

This statement shows that the corresponding angles of triangles CDE and ABE are congruent, which is essential in proving that triangle ABE is congruent to triangle CDE.