Question

Statements Reasons 1. BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. ??? Fill in the missing reason for the proof. A) SSS Congruence Theorem B) SSS Similarity Theorem C) AA Similarity Postulate D) SAS Congruence Postulate

Answer 1

The correct option is;

C) AA Similarity Postulate

Explanation:

The given parameters are;

BE║CD Given

∠A is congruent to ∠A Reflective property

∠ACD is congruent to ∠ABE Corresponding angles formed by parallel lines and a transversal

∠ADC is congruent to ∠AEB Corresponding angles formed by parallel lines and a transversal

ΔABE ~ ΔACD AA Similarity Postulate

When two angles of one triangle are equal to the corresponding two angles of another triangle, given that the third angle of both triangles are also equivalent based on sum of angles of a triangle postulate, the two triangles are said to be similar based on Angle-Angle (AA) Similarity Postulate.