Question 17
In given figure ∠1 = ∠2 and ∆NSQ ≅ ∆MTR , then prove that ∆PTS ~ ∆ PRQ .
Given: ∠ 1 = ∠ 2
& ΔNSQ ≅ ΔMTR
To Prove: ΔPTS ∼ PRQ
Proof:
Given ΔNSQ ≅ ΔMTR
∴ ∠ NQS = ∠ MRT
i.e. ∠ PQR = ∠ PRQ
Now,
In Δ PST
By angle sum property
∠ P + ∠ 1 + ∠ 2 = 180°
Since ∠ 1 = ∠ 2 given
∠ P + ∠ 1 + ∠ 1 = 180°
∠ P + 2 ∠ 1 = 180°
In Δ PQR
By angle sum property
∠ P + ∠ PQR + ∠ PRQ = 180°
From (1), ∠ PQR = ∠ PRQ
∠ P + ∠ PQR + ∠ PQR = 180°
∠ P + 2 ∠ PQR = 180°
Right side of (2) and (3) are same
So, from (2) and (3)
∠ P + 2 ∠ 1 = ∠ P + 2 ∠ PQR
2 ∠ 1 = 2 ∠ PQR
∠ 1 = ∠ PQR
In ΔPTS & Δ PRQ
∠P = ∠P (Common angle)
∠ PST = ∠ PQR (From (4))
∴ ΔPTS ∼ PRQ (AA similarity)
Hence proved

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!