Question

Prove the similarity of \triangle ABC with respect to \triangle PQR.

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asked 2021-08-05
To prove: The similarity of \(\displaystyle\triangle{A}{B}{C}\) with respect to \(\displaystyle\triangle{P}{Q}{R}\).
Given information: Here, we have given that acute angles of both right angles are congruent (\(\displaystyle\Rightarrow\angle{A}{C}{B}\stackrel{\sim}{=}\angle{P}{R}{Q}\))
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Answers (1)

2021-08-06
Proof: In \(\displaystyle\triangle{A}{B}{C}\ {\quad\text{and}\quad}\ \triangle{P}{Q}{R}\)
\(\displaystyle\angle{A}{C}{B}\stackrel{\sim}{=}\angle{P}{R}{Q}\) (Given)
\(\displaystyle\angle{A}{B}{C}\stackrel{\sim}{=}\angle{P}{Q}{R}\) (Right Angles)
\(\displaystyle\Rightarrow\triangle{A}{B}{C}\sim\triangle{P}{Q}{R}\) (By AA Similarity Rule)
\(\displaystyle\therefore\) The triangles are similar.
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