Question

Given: AB ≅ AE; BC ≅ DE Prove: ∠ACD ≅ ∠ADC Complete the paragraph proof. We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then determine △ABC ≅ △AED by . Because of CPCTC, segment AC is congruent to segment . Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.

Answer 1

The proof establishes that triangles ABC and AED are congruent using the Angle-Side-Angle postulate, leading to the conclusion that triangle ACD is isosceles and therefore the angles ∠ACD and ∠ADC are congruent.

Step-by-step explanation:

We are given that AB ≅ AE and BC ≅ DE, implying that triangle ABE is an isosceles triangle. According to the Isosceles Triangle Theorem, the base angles of an isosceles triangle are congruent, which means that ∠ABE ≅ ∠AEB. With congruent corresponding angles and sides, we can use the Angle-Side-Angle (ASA) postulate to conclude that △ABC ≅ △AED.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC), segment AC is congruent to segment AD. Hence, triangle ACD is an isosceles triangle. Since the base angles of an isosceles triangle are congruent, we can deduce that ∠ACD ≅ ∠ADC, completing the proof.

Answer 2

SAS

AD

Step-by-step explanation

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