Question

32. If S is a point on side PQ of a APQR such that PS = QS = RS, then (a) PR. QR = RS2 (b) QS2 + RS2 = QR (C) PR2 + QR2 = PQ2 (d) PS2 + RSP = PR2 - -​

Answer 1

Step-by-step explanation:

Question

If S is a point on side PQ of a APQR such that PS = QS = RS, then

(a) PR. QR = RS2

(b) QS2 + RS2 = QR

(C) PR2 + QR2 = PQ2

(d) PS2 + RSP = PR2

Solution

In ΔPQR

PS=SQ=RS

And , in ΔPSR , PS=SR

∴∠1=∠P [Angles opposite to equal sides in a triangle are equal]

Similarly , in ∠SRQ ,

RS=SQ (given)

∠Q=∠2

Now , in ΔPQR ,

∠P+∠Q+∠PRQ=180° [By Angle sum property of a triangle]

$\sf⇒∠1+∠2+(∠1+∠2)=180° \\ \sf⇒2(∠1+∠2)=180° \\\sf⇒∠1+∠2=90° \\ \sf⇒∠PRQ=90°$

$\sf \: By \: Pythagoras \: theorem , \: we \: have PQ^2 \\ \sf=PR^2+RQ^2$

Hence the correct option is (c)