Question

To write: The plan to prove \angle1\cong\angle2, use the given figure is as follows

Congruence
ANSWERED
asked 2021-07-31
To write: The plan to prove \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\).
Given:
The given figure is as follows.
image

Answers (1)

2021-08-01
Calculation:
By SSS Congruence Theorem, prove that \(\displaystyle\triangle{Q}{S}{V}\stackrel{\sim}{=}\triangle{Q}{T}{V}\).
Then, state that \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{Q}{T}{V}\).
Use the Vertical Angles Theorem, \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{1},\ {\quad\text{and}\quad}\ \angle{Q}{T}{V}\stackrel{\sim}{=}\angle{2}\).
Therefore, by the Transitive Property of Congruence to prove that \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\).
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