Question

Prove in the following figure, triangles ABC and ADC are congruent.

Congruence
ANSWERED
asked 2021-07-20
To prove: In the following figure, triangles ABC and ADC are congruent.
Given:
Figure is shown below:
image
It is provided that \(\displaystyle\angle{B}{A}{C}=\angle{D}{A}{C}\ {\quad\text{and}\quad}\ \angle{B}{C}{A}=\angle{D}{C}{A}\).

Expert Answers (1)

2021-07-21
Formula used:
Angle - Side - Angle (ASA) - If two angles and the included side of one triangle are equal, respectively, to two angles and the included side of a second triangle, then the triangles are congruent.
Proof:
Make the table of statement and reason for \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{A}{D}{C}\).
\(\displaystyle\angle{B}{A}{C}=\angle{D}{A}{C}\) (Given)
\(\displaystyle\angle{B}{C}{A}=\angle{D}{C}{A}\) (Given)
AC=AC (Reflexive property)
\(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{A}{D}{C}\) (ASA Congruence property)
Thus, the \(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{A}{D}{C}\) by the ASA congruence property.
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