Question

Given Segment EC is perpendicular to Segment AD.

Segment BD is perpendicular to segment AC. Segment ED is congruent to Segment BC. Prove triangle DCB is congruent to triangle CDE. Pls help!

Answer 1

To prove that triangle DCB is congruent to triangle CDE, we can use the congruent triangles postulate which states that if two corresponding sides and the included angle of one triangle are congruent to two corresponding sides and the included angle of another triangle, then the two triangles are congruent.

Step-by-step explanation:

To prove that triangle DCB is congruent to triangle CDE, we can use the congruent triangles postulate which states that if two corresponding sides and the included angle of one triangle are congruent to two corresponding sides and the included angle of another triangle, then the two triangles are congruent.

1. Given: Segment EC is perpendicular to Segment AD.
2. Segment BD is perpendicular to segment AC.
3. Segment ED is congruent to Segment BC.

To prove: Triangle DCB is congruent to triangle CDE.

1. By definition, Segment EC is perpendicular to Segment AD and Segment BD is perpendicular to segment AC. Therefore, angle CED is congruent to angle BDC.

2. Segment ED is congruent to Segment BC.

3. By the congruent triangles postulate, triangle DCB is congruent to triangle CDE.