Question

Given: 2 ≅ 5, AB ≅ DE
Prove: BC ≅ EC

Answer 1

See explanation

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.