Question

Given: 2 ≅ 5, AB ≅ DE
Prove: BC ≅ EC

Answer 1

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABC and DEC. In these triangles,

• $\angle 2\cong \angle 5$ - given;
• $AB\cong DE$ - given;
• $\angle 3\cong \angle 4$ - as vertical angles when lines AD and BE intersect.

Thus, by AAS postulate, triangles ABC and DEC are congruent. Congruent triangles have congeruent corresponding sides.

So,

$BC\cong EC$

The Angle Angle Side postulate (AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.