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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 [state congruence criterion, such as SAS or ASA]. Because of CPCTC (Corresponding Parts of Congruent Triangles are Congruent), segment AC is congruent to segment [fill in the missing segment]. Triangle ACD is an isosceles triangle based on the definition of an isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.

Answer :

Final answer:

Triangle ABC is congruent to triangle AED by SAS congruence, and segment AC congruent to segment AD by CPCTC.

Explanation:

We can determine triangle ABC equals triangle AED by Side Angle Side (SAS) congruence because AB is congruent to AE, angle ABE is congruent to angle AEB, and BC is congruent to DE. Thus, we have two sides, and the angle between them is congruent. Because Corresponding Parts of Congruent Triangles are Congruent (CPCTC), segment AC is congruent to segment AD. Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, angle ACD equals angle ADC.

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Rewritten by : Jeany

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