Final answer:
To prove that △ADC is congruent to △BEC, we can use the Side-Side-Side (SSS) congruence criterion. to prove that △AEC is congruent to △BDC, we can use the Side-Angle-Side (SAS) congruence criterion.
Step-by-step explanation:
To prove that △ADC is congruent to △BEC, we can use the Side-Side-Side (SSS) congruence criterion. Since AC is equal to BC, AD is equal to BE, and CD is common to both triangles, we have two pairs of corresponding sides and one pair of corresponding angles that are congruent. Therefore, △ADC ≅ △BEC.
To prove that △AEC is congruent to △BDC, we can use the Side-Angle-Side (SAS) congruence criterion. We know that AC is equal to BC, ∠A is equal to ∠B (both are 90 degrees), and AD is equal to BE. Therefore, △AEC ≅ △BDC.