Question

\angle HGJ\cong \angle KJG, \angle KGJ\cong \angle HJG show that two sides are congruent.

Congruence
ANSWERED
asked 2021-07-26
To show that two sides are congruent.
Given information:
\(\displaystyle\angle{H}{G}{J}\stackrel{\sim}{=}\angle{K}{J}{G}\)
\(\displaystyle\angle{K}{G}{J}\stackrel{\sim}{=}\angle{H}{J}{G}\)

Answers (1)

2021-07-27

Formula used:
The below property is used:
Two triangles are congruent by ASA congruence rule.
Proof:
From figure, we get
image
It is given that,
\(\displaystyle\angle{H}{G}{J}\stackrel{\sim}{=}\angle{K}{J}{G}\)
\(\displaystyle\angle{K}{G}{J}\stackrel{\sim}{=}\angle{H}{J}{G}\)
By reflexive property, we get
\(\displaystyle\overline{{{G}{J}}}\stackrel{\sim}{=}\overline{{{G}{J}}}\)
By ASA congruence rule, we get
\(\displaystyle\triangle{G}{H}{J}\stackrel{\sim}{=}\triangle{J}{K}{G}\)
As corresponding parts of congruent triangles are congruent, we get
\(\displaystyle\overline{{{H}{G}}}\stackrel{\sim}{=}\overline{{{K}{J}}}\)

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