one angle of a triangle is equal to one angle of another triangle and the bisector of these angles divides the opposite sides in the same ratio than prove that the triangles are similar.
Answers
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Answer:
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)
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)