Angles Q and R of a - PQR are 25- and 65- Write which of the following is true-i PQ 2- QR 2- RP 2ii PQ 2- RP 2- QR 2iii RP 2- QR 2- PQ 2

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Standard VII

Mathematics

Important Properties of Triangles

Angles Q and ...

Question

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

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Solution

The sum of the measures of all interior angles of a triangle is 180º.

∠PQR + ∠PRQ + ∠QPR = 180º

25º + 65º + ∠QPR = 180º

90º + ∠QPR = 180º

∠QPR = 180º − 90º = 90º

Therefore, Δ PQR is right-angled at point P.

Hence, (PR)² + (PQ)² = (QR)²

Thus, (ii) is true.

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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. 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}

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° and 65°. Write which of the following is true: (i) PQ2 + QR2= RP2 (ii) PQ2 + RP2= QR2 (iii) RP2 + QR2= PQ2

The sum of the measures of all interior angles of a triangle is 180º. ∠PQR + ∠PRQ + ∠QPR = 180º 25º + 65º + ∠QPR = 180º 90º + ∠QPR = 180º ∠QPR = 180º − 90º = 90º Therefore, Δ PQR is right-angled at point P. Hence, (PR)2 + (PQ)2 = (QR)2 Thus, (ii) is true.

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

The sum of the measures of all interior angles of a triangle is 180º.

∠PQR + ∠PRQ + ∠QPR = 180º

25º + 65º + ∠QPR = 180º

90º + ∠QPR = 180º

∠QPR = 180º − 90º = 90º

Therefore, Δ PQR is right-angled at point P.

Hence, (PR)² + (PQ)² = (QR)²

Thus, (ii) is true.