Angles Q and R of a - PQR are 25 - and 65 - Write which of the following is true- - a PQ2 - QR2 - RP2- b PQ2 - RP2 - QR2- c RP2 - QR2 - PQ2 -

The correct option is B bIn Δ PQR ∠ Q=25^∘,∠ R=65^∘ The sum of angles is 180^∘ in a triangle. ∠ P+∠ Q+ ∠ R=180 ∠ P+25+65=180 ∠ P=90^ ...

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Byju's Answer

Standard IX

Mathematics

If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Angles Q and ...

Question

Angles Q and R of a $Δ P Q R$ are $25^{\circ} a n d 65^{\circ}$ . Write which of the following is true:
$\begin{matrix} (a) P Q^{2} + Q R^{2} = R P^{2} (b) P Q^{2} + R P^{2} = Q R^{2} (c) R P^{2} + Q R^{2} = P Q^{2} \end{matrix}$

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Solution

The correct option is B b
In $Δ P Q R$

$∠ Q = 25^{\circ}, ∠ R = 65^{\circ}$

The sum of angles is $180^{\circ}$ in a triangle.

$⟹ ∠ P + ∠ Q + ∠ R = 180 ∠ P + 25 + 65 = 180 ∠ P = 90^{\circ}$

So $Δ P Q R$ is a right-angled triangle

By Pythagoras theorem,
$⟹ P Q^{2} + R P^{2} = Q R^{2}$

Suggest Corrections

Similar questions

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ² + QR²= RP²

(ii) PQ² + RP²= QR²

(iii) RP² + QR²= PQ²

Question 6
Angles Q and R of a $Δ$ PQR are $25^{\circ}$ and $65^{\circ}$ .
Write which of the following is true:
(i) $P Q^{2} + Q R^{2} = R P^{2}$
(ii) $P Q^{2} + R P^{2} = Q R^{2}$
(iii) $R P^{2} + Q R^{2} = P Q^{2}$

Q. In

Δ P Q R

, if

P R^{2} = P Q^{2} + Q R^{2}

, prove that

∠ Q

is right angle.

Q. In

∆

PQR,

∠

Q = 90

°

, seg QM is the median. PQ² + QR² = 169. Draw a circumcircle of

∆

PQR.

Q. In the following figure angle

P Q R = 90^{\circ}

and

¯ ¯¯¯¯¯¯ ¯ S Q

is perpendicular to PR. Show that

Q R^{2} \times P S^{2} = P Q^{2} \times Q R^{2}

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Angles Q and R of a ΔPQR are 25∘and65∘. Write which of the following is true:(a)PQ2+QR2=RP2(b)PQ2+RP2=QR2(c)RP2+QR2=PQ2

The correct option is B bIn ΔPQR∠Q=25∘,∠R=65∘The sum of angles is 180∘ in a triangle.⟹∠P+∠Q+∠R=180∠P+25+65=180∠P=90∘So ΔPQR is a right-angled triangle By Pythagoras theorem,⟹PQ2+RP2=QR2

Angles Q and R of a $Δ P Q R$ are $25^{\circ} a n d 65^{\circ}$ . Write which of the following is true:
$\begin{matrix} (a) P Q^{2} + Q R^{2} = R P^{2} (b) P Q^{2} + R P^{2} = Q R^{2} (c) R P^{2} + Q R^{2} = P Q^{2} \end{matrix}$