Question

What proves angle BDE is congruent to CDE. ∆ADB and ∆ADC are congruent.

Answer 1

Answer: We will use the SAS (SIDE-ANGLE-SIDE) to prove that the two triangles are congruent. This states that if two sides and the included angle in one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

First line

First column: AB is congruent to CB Second column: Given

Second line

First column: angle ABD is congruent to angle CBD Second column: Given

At this point we have the SIDE-ANGLE portion of SAS. We just need the other side. We can see from the given angles that they both share a side...BD.

Third Line

First column: BD is congruent to BD Second column: Reflexive property

All that is left is to state SAS.

Fourth Line

First Column: Triangle ABD is congruent to triangle CBD Second column: SAS (from lines 1,2,3)

Answer 2

∆ADB and ∆ADC are congruent by the AAS theorem

What proves angle BDE is congruent to CDE.

From the question, we have the following parameters that can be used in our computation:

The triangles ADB and ADC

These triangles are congruent by the AAS theorem

This is so because the two triangles have two angles and a non-included side that are congruent to the corresponding angles and non-included side of one another

Hence, ∆ADB and ∆ADC are congruent by the AAS theorem