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High School
Geometry
High school geometry
Similarity

tinfoQ

Answered question

2021-05-16

To prove : The similarity of $△ N R T$ with respect to $△ N S P$ .
Given information: Here, we have given that $\overset{―}{S P}$ is altitude to $\overset{―}{N R} and \overset{―}{R T}$ is altitude to $\overset{―}{N S}$ .

Answer & Explanation

dieseisB

Skilled2021-05-18Added 85 answers

Proof: As,

\overset{―}{S P}

is altitude to

\overset{―}{N R}

\Rightarrow ∠ S P N = 90^{\circ}

Similarity, as

\overset{―}{R T}

is altitude to

\overset{―}{N S}

\Rightarrow ∠ R T N = 90^{\circ}

\Rightarrow ∠ R T N \tilde{=} ∠ S P N

Now, In

△ N R T and △ N S P

∠ R T N \tilde{=} ∠ S P N

(Proved above)

∠ N \tilde{=} ∠ N

(Common)

\Rightarrow △ N R T \sim △ N S P

(By AA Similarity Rule)

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