In ∆PQR, if QS is the angle bisector of ∠Q, then show that A(∆PQS)/A(∆QRS) = PQ/QR. (Hint: Draw QT ⊥ PR)

Question

In ∆PQR, if QS is the angle bisector of ∠Q, then show that .

\(\cfrac{A(∆PQS)}{A(∆QRS)}=\cfrac{PQ}{QR}\). (Hint: Draw QT ⊥ PR)

A(∆PQS)/A(∆QRS) = PQ/QR

Answer 1

Proof:

In ∆PQR,

Ray QS is the angle bisector of ∠PQR ---- [Given]

\(\therefore\) PQ/QR = PS/SR ---- (i) [By property of angle bisector of a triangle]

Height of ∆PQS = Height of ∆QRS = QT

---[Ratio of areas of two triangles having equal heights is equal to the ratio of their corresponding bases]