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
Image with alt text: Modifying over Upper A Upper B with bar approximately-equals Modifying over Upper C Upper D with bar
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Based on the Given information, the statement that can be proved by CPCTC and is needed to work toward the prove statement is:
Modifying over Upper A Upper B with bar approximately-equals Modifying over Upper C Upper D with bar.
The correct statement that can be proven by CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and is needed to work toward the prove statement is:
Modifying over Upper A Upper D with bar approximately-equals Modifying over Upper C Upper B with bar
To determine which statement can be proved using CPCTC and is needed to work toward the prove statement, we need to identify which statement involves corresponding parts of congruent triangles.
In this case, the given information tells us that triangle ABD is congruent to triangle CDB.
So, we need to find a statement that involves corresponding parts of these congruent triangles.
Looking at the given figure, we can see that angle ABD corresponds to angle CDB and angle AED corresponds to angle CED.
Therefore, the statement "angle DCE ≈ angle BAD" can be proved using CPCTC and is needed to work toward the prove statement "triangle ABE congruent to triangle CDE".