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
Transcript text: In the figure, $\triangle E B A \cong \triangle E D C$.
Because CPCTC, which relationships are true? Check all that apply.
$\overline{\mathrm{AE}} \cong \overline{\mathrm{CE}}$
$\angle B A E \cong \angle D C E$
$\angle C D E \simeq \angle B A E$
$\overline{\mathrm{AB}} \cong \overline{\mathrm{BE}}$
$\overline{A C} \cong \overline{B D}$
Solution
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.