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.
Accepted Solution
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Answer:In isosceles triangle - the base angles are congruent.so, ∠ACD ≅ ∠ADCStep-by-step explanation:Given: AB ≅ AE, BC ≅ DE If AB = AEThen, ΔABE is a isosceles triangle.The base angle of isosceles triangle are same.So, ∠B = ∠ENow in ΔABC and ΔAEDBC ≅ DE , ∠B = ∠E, AB ≅ AEFrom side angle side theoremΔABC ≅ ΔAEDThen, AC ≅ ADHence, ΔACD is a isosceles triangle.And we know that the base angle of isosceles triangle are same.So, ∠ACD ≅ ∠ADC proved