Question

if one angle of a triangle is equal to one angle of other triangle and side including this angles are proportional then the two Triangles are similar. Prove this theorem ​

Answer 1

Step-by-step explanation:

Given: △ABC and △PQR

∠A = ∠P

AD and PS bisects ∠A and ∠P respectively.

BD = QS

DC = SR

To prove: △ABC ~  △PQR

Proof : In △ABC and △PQR

AD bisects ∠A

∴ AB = BD (Angle bisector theorem) ......(1)

AC = DC

Similarly in △PQR,

PQ = QS (Angle bisector theorem).......(2)

PR = SR

But BD = QS (given)

DC = SR

∴ According to the equation (1) and (2)

AB = PQ = AB = AC

AC = PR = PQ = PR

∠A and ∠P (given)

∴ △ABC ~ △PQR (SAS similarity)

Answer 2

Answer:

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