Question

To prove : The similarity of \triangle NRT with respect to \triangle NSP.Given information: Here,

Similarity
ANSWERED
asked 2021-05-16

To prove : The similarity of \(\displaystyle\triangle{N}{R}{T}\) with respect to \(\displaystyle\triangle{N}{S}{P}\).
Given information: Here, we have given that \(\displaystyle\overline{{{S}{P}}}\) is altitude to \(\displaystyle\overline{{{N}{R}}}\ {\quad\text{and}\quad}\ \overline{{{R}{T}}}\) is altitude to \(\displaystyle\overline{{{N}{S}}}\).

Expert Answers (1)

2021-05-18
Proof: As, \(\displaystyle\overline{{{S}{P}}}\) is altitude to \(\displaystyle\overline{{{N}{R}}}\),
\(\displaystyle\Rightarrow\angle{S}{P}{N}={90}^{{\circ}}\)
Similarity, as \(\displaystyle\overline{{{R}{T}}}\) is altitude to \(\displaystyle\overline{{{N}{S}}}\),
\(\displaystyle\Rightarrow\angle{R}{T}{N}={90}^{{\circ}}\)
\(\displaystyle\Rightarrow\angle{R}{T}{N}\stackrel{\sim}{=}\angle{S}{P}{N}\)
Now, In \(\displaystyle\triangle{N}{R}{T}\ {\quad\text{and}\quad}\ \triangle{N}{S}{P}\)
\(\displaystyle\angle{R}{T}{N}\stackrel{\sim}{=}\angle{S}{P}{N}\) (Proved above)
\(\displaystyle\angle{N}\stackrel{\sim}{=}\angle{N}\) (Common)
\(\displaystyle\Rightarrow\triangle{N}{R}{T}\sim\triangle{N}{S}{P}\) (By AA Similarity Rule)
36
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...