Q. 73.6( 24 Votes )

# In figure 3.62, seg PT is the bisector of ∠QPR. A line through R intersects ray QP at point S. Prove that PS = PR

Answer :

Given: PT is angle bisector of ∠QPR

⇒ ∠QPT = ∠RPT

A line through R parallel to PT intersects ray QP at S

RS || PT

To Prove: PS = PR

Proof:

PT is angle bisector of ∠QPR

⇒ ∠QPT = ∠RPT

∠QPR = ∠QPT + ∠RPT

∠QPR = 2∠RPT (1)

RS || PT, PR is the transversal

So, ∠RPT = ∠PRS [Alternate interior angles] (2)

For ΔPRS ∠RPQ is the remote exterior angle.

∠PSR + ∠PRS = ∠QPR

Substituting (1) and (2) in the above equation

∠RPT + ∠PSR = 2∠RPT

⇒ ∠PSR = ∠RPT (3)

From (2) and (3)

∠PRS = ∠PSR

⇒ PS = PR [Sides opposite to equal angles are equal]

Rate this question :

In ΔPQR, ∠Q =90^{0}, PQ = 12, QR = 5 and QS is a median. Find *t*(QS).

In figure 3.49, ∠RST = 56°, seg PT ⊥ ray ST, seg PT ⊥ ray ST, seg PR ⊥ ray SR and PR ≅ seg PT Find the measure of ∠RSP. State the reason for your answer.

MHB - Math Part-II

In ΔPQR, ∠P = 70° ∠Q = 65° then find ∠R.

MHB - Math Part-IIIn figure 3.10, line AB || line DE. Find the measures of ∠DRE and ∠ARE using given measures of some angles.

MHB - Math Part-II

In figure 3.8, ∠ACD is an exterior angle of ΔABC. ∠B = 40°, ∠A = 70°. Find the measure of ∠ACD.

MHB - Math Part-II

The measures of angles of a triangle are x°, (x – 20)°, (x – 40)°. Find the measure of each angle.

MHB - Math Part-II