Question

S is a point on side PQ of a PQR such that PQ=QS =RS, then
(a) PR×QR =RS ^2
(b) QS^2+RS^2= QR^2
(c) PR^2+QR^2=PQ^2
(d)PS^2×RS^2= PR^2

Answer this along with step by step explanation
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Answer 1

Answer:

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S is a point on side PQ of a PQR such that PQ=QS =RS, then

$(a) \: {pr} \times qr = {rs}^{2} \\ (b) {qs}^{2} + {rs}^{2} = {qr}^{2} \\ (c) \: {pr}^{2} + {qr}^{2} = {pq}^{2} \\ (d) \: {ps}^{2} \times {rs}^{2} = {pr}^{2}$

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In ∆PQR

PS = QS + RS (i)

In ∆PSR

PS = RS ….. [from Equation (i)]

∠1 = ∠2 Equation (ii)

Similarly,

In ∆RSQ,

∠3 = ∠4 Equation (iii) [Corresponding angles of equal sides are equal]

[By using Equations (ii) and (iii)]

Now in, ∆PQR,

sum of angles = 180°

⇒∠P + ∠Q + ∠R = 180°

⇒ ∠2 + ∠4 + ∠1 + ∠3 = 180°

⇒ ∠1 + ∠3 + ∠1 + ∠3 = 180°

⇒∠2 (1 + ∠3) = 180°

⇒∠1 + ∠3 = (180°)/2 = 90°

∴ ∠R = 90°

In ∆PQR, by Pythagoras theorem,

${pr}^{2} + {qr}^{2} = {pq}^{2}$

So correct option is (c)

Answer 2

Answer:

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