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Home » In figure, if ∠1 =∠2 and ΔNSQ = ΔMTR, then prove that ΔPTS ~ ΔPRQ.
In figure, if ∠1 =∠2 and ΔNSQ = ΔMTR, then prove that ΔPTS ~ ΔPRQ.
CBSE | Class 10 | Exercise 6.3 | Maths | NCERT Exemplar | Triangles
In figure, if ∠1 =∠2 and ΔNSQ = ΔMTR, then prove that ΔPTS ~ ΔPRQ.

NCERT Exemplar Solutions Class 10 Maths Chapter 6 Ex. 6.3-6

Solution:

According to the given question,

\text{ }\Delta NSQ~\cong ~\Delta MTR

\angle 1\text{ }=~\angle 2

Since,

\Delta NSQ\text{ }=\text{ }\Delta MTR

As a result,

SQ\text{ }=\text{ }TR….(i)

Also,

\angle 1\text{ }=~\angle 2~\Rightarrow ~PT\text{ }=\text{ }PS….(ii)[as we know, sides opposite to equal angles are also equal]

From eq. (i) and eq. (ii).

PS/SQ\text{ }=\text{ }PT/TR

⇒ ST || QR

If a line is drawn parallel to triangle’s one side to intersect the other two sides in distinct points, then the other two sides are also divided in the same ratio according to the converse of basic proportionality theorem.

\therefore ~\angle 1\text{ }=\text{ }PQR

And

\angle 2\text{ }=~\angle PRQ

In triangles PTS and PRQ.

\angle P\text{ }=~\angle P[Common angles]

\angle 1\text{ }=~\angle PQR (proved)

\angle 2\text{ }=~\angle PRQ(proved)

\therefore ~\Delta PTS\sim \Delta PRQ

[By AAA similarity criteria]

As a result, proved.

i

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