Question

In fig angle 1 = angle 2 triangle PTS similar to PRQ

Answer 1

Answe

Step-by-step explanation:

given: ΔNSQ≅ΔMTR

and ∠1=∠2

to prove:ΔPTS similar toΔPQR

proof: ∠Q=∠R (cpct ∵ΔNSQ≅ΔMTR)

in ΔPST;

∠P+∠1+∠2=180 (A.S.P)--------(1)

in ΔPQR;

∠P+∠PQR+∠PRQ=180(A.S.P)--------(2)

by (1) &(2)

∠P+∠1+∠2=∠P+∠PQR+∠PRQ

∠1+∠2=∠PQR+∠PRQ

2∠1=2∠PQR

∴∠1=∠PQR--------------------(A)

∠P=∠P(common)-------(B)

by (A)&(B)

ΔPTS similar to ΔPQR