Questions: In the figure, triangle EBA is congruent to triangle EDC. Because CPCTC, which relationships are true? Check all that apply. - AE is congruent to CE - angle BAE is congruent to angle DCE - angle CDE is similar to angle BAE - AB is congruent to BE - AC is congruent to BD

In the figure, triangle EBA is congruent to triangle EDC.

Because CPCTC, which relationships are true? Check all that apply.
- AE is congruent to CE
- angle BAE is congruent to angle DCE
- angle CDE is similar to angle BAE
- AB is congruent to BE
- AC is congruent to BD
Transcript text: In the figure, $\triangle E B A \cong \triangle E D C$. Because CPCTC, which relationships are true? Check all that apply. $\overline{\mathrm{AE}} \cong \overline{\mathrm{CE}}$ $\angle B A E \cong \angle D C E$ $\angle C D E \simeq \angle B A E$ $\overline{\mathrm{AB}} \cong \overline{\mathrm{BE}}$ $\overline{A C} \cong \overline{B D}$
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Solution

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Solution Steps

Step 1: Analyze the given information

We are given that triangle EBA is congruent to triangle EDC (ΔEBA ≅ ΔEDC). Corresponding parts of congruent triangles are congruent (CPCTC).

Step 2: Identify corresponding parts

The order of the vertices in the congruence statement tells us which parts correspond:

  • EB corresponds to ED
  • BA corresponds to DC
  • AE corresponds to EC
  • ∠EBA corresponds to ∠EDC
  • ∠BAE corresponds to ∠DCE
  • ∠BEA corresponds to ∠DEC
Step 3: Identify the true relationships

Based on the correspondences and CPCTC, the following relationships are true:

  • AE ≅ CE
  • ∠BAE ≅ ∠DCE

Final Answer:

The true relationships are AE ≅ CE and ∠BAE ≅ ∠DCE.

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