Question

Find the congruence criteria \overline{AB}\cong\overline{DC}\ and\ \overline{AC}\cong\overline{DB} used to prove the triangles are congruent

Congruence
ANSWERED
asked 2021-07-13
To find: congruent criteria used to prove that the triangles are congruent.
Given information: \(\displaystyle\overline{{{A}{B}}}\stackrel{\sim}{=}\overline{{{D}{C}}}\ {\quad\text{and}\quad}\ \overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{D}{B}}}\)
image

Expert Answers (1)

2021-07-14
Consider \(\displaystyle\triangle{A}{B}{C},\triangle{D}{C}{B}\)
\(\displaystyle\overline{{{A}{B}}}\stackrel{\sim}{=}\overline{{{D}{C}}}\) (Given)
\(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{D}{B}}}\) (Given)
\(\displaystyle\overline{{{B}{C}}}\stackrel{\sim}{=}\overline{{{C}{B}}}\) (common side of \(\displaystyle\triangle{A}{B}{C},\triangle{D}{C}{B}\))
Therefore,
\(\displaystyle\triangle{A}{B}{C}\stackrel{\sim}{=}\triangle{D}{C}{B}\) (SSS congruence criteria)
Also.
Congruent triangles basically overlap each other.
So, \(\displaystyle\triangle{A}{B}{C},\triangle{D}{C}{B}\) is a pair of overlapping triangles.
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