Q4 of 76 Page 10

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.


Given that PQR is a triangle


Such that,


PQ = PR


And, S is any point on side PQ and ST ‖ QR


We have to prove PS = PT


Since,


PQ = PR


PQR is isosceles


∠Q = ∠R


Or, ∠PQR = ∠PRQ


Now,


∠PST = ∠PQR


And,


∠PTS = ∠PRQ (Corresponding angles as ST ‖ QR)


Since,


∠PQR = ∠PRQ


∠PST = PTS


Now, in


∠PST = ∠PTS


Therefore, is an isosceles triangle


PS = PT


More from this chapter

All 76 →
2

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

 3

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

 5

In a Δ ABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.

 6

P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that the triangle BPQ is isosceles.