Question

in the figure, △eba≅△edc. because cpctc, which relationships are true? check all that apply. □ae≅ce □∠bae≅∠dce □∠cde≅∠bae □ab≅be □ac≅bd

Explanation:

Step1: Recall CPCTC (Corresponding - Parts of Congruent Triangles are Congruent)

If \(\triangle EBA\cong\triangle EDC\), then corresponding sides and angles are congruent.

Step2: Analyze corresponding sides

The corresponding sides of congruent triangles \(\triangle EBA\) and \(\triangle EDC\) are: \(AE\) and \(CE\) are corresponding sides, \(AB\) and \(CD\) are corresponding sides, \(BE\) and \(DE\) are corresponding sides. Also, \(AC\) and \(BD\) are not corresponding sides in the congruent - triangle pair \(\triangle EBA\) and \(\triangle EDC\).

Step3: Analyze corresponding angles

The corresponding angles of congruent triangles \(\triangle EBA\) and \(\triangle EDC\) are: \(\angle BAE\) and \(\angle DCE\), \(\angle ABE\) and \(\angle CDE\), \(\angle AEB\) and \(\angle CED\).

Answer:

\(\angle BAE\cong\angle DCE\), \(AE\cong CE\)