Question

Complete all statements and reasons for the following proof problem \angle R and \angle V are right angles. \angle 1\cong\angle 2.

Congruence
ANSWERED
asked 2021-07-25
Complete all statements and reasons for the following proof problem.
Given:
\(\displaystyle\angle{R}\) and \(\displaystyle\angle{V}\) are right angles. \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\)
Prove: \(\displaystyle\triangle{R}{S}{T}\stackrel{\sim}{=}\triangle{V}{S}{T}\)
image

Expert Answers (1)

2021-07-26
Step 1
Given: \(\displaystyle\angle{R}=\angle{V}={90}^{{\circ}},\angle{1}\stackrel{\sim}{=}\angle{2}\)
For proving given thing, we take \(\displaystyle\triangle{R}{S}{T}\ {\quad\text{and}\quad}\ \triangle{V}{S}{T}\)
Step 2
So, \(\displaystyle\triangle{R}{S}{T}\ {\quad\text{and}\quad}\ \triangle{V}{S}{T}\)
\(\displaystyle\angle{R}=\angle{V}\) (given)
\(\displaystyle\angle{1}=\angle{2}\) (given)
ST=ST (common)
So, by ASA congruency rule
\(\displaystyle\triangle{R}{S}{T}\stackrel{\sim}{=}\triangle{V}{S}{T}\)
Hence, \(\displaystyle\triangle{R}{S}{T}\ {\quad\text{and}\quad}\ \triangle{V}{S}{T}\) are congruence.
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