Q. 53.8( 8 Votes )

In ∆PQR and ∆MST, P = 55°, Q = 25°, M = 100° and S = 25°. Is ∆QPR ∆TSM? Why? (True)

Answer :

We know that,

The sum of three angles of a triangle is 180°.


In ∆PQR,


P + Q + R = 180°


55° + 25° + R = 180°


⇒ ∠R = 180° - (55° + 25°) = 180°- 80° = 100°


Similarly, in ∆TSM,


T + S + M = 180°


T + 25° + 100° = 180°


⇒ ∠T = 180°- (25° + 100°)


T = 180° - 125° = 55°




In ∆PQR and ∆TSM,


P = T,


Q = S


And


R = M


So, ∆PQR TSM


Since, all corresponding angles are equal


Hence,


∆QPR is similar to ∆TSM,


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