For the - PQR- PA is the angle bisector of - P- then AR-

Here, PA is the angle bisector of ∠ P. In nbsp; nbsp;Δ PQA and Δ PRA, PQ=PR ∠ QPA = ∠ RPA PA is common nbsp;Δ PQA≅Δ PRA. ∴ The corresponding side length ...

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Byju's Answer

Standard VII

Mathematics

Angle Angle Side or A-A-S Congruence

For the Δ PQR...

Question

For the $Δ P Q R, P A$ is the angle bisector of $∠ P$ , then $A R =$

P Q

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\frac{Q R}{2}

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\frac{3 Q R}{4}

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Solution

The correct option is B $\frac{Q R}{2}$

Here, $P A$ is the angle bisector of $∠ P$ .
In $Δ P Q A$ and $Δ P R A$ ,
$P Q = P R$
$∠ Q P A = ∠ R P A$
$P A$ is common
$Δ P Q A ≅ Δ P R A$ .
$∴$ The corresponding side lengths and angles will be equal for both the triangles.
$\Rightarrow Q A = R A$
$\Rightarrow 2 \times Q A = Q R \Rightarrow Q A = \frac{Q R}{2}$
Or $A R = \frac{Q R}{2}$

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Similar questions

Δ P Q R

is an equilateral triangle and

P A

is the angle bisector of

∠ P

, then

Δ P Q A ≅ Δ P R A

Q. Choose the correct answer from the alternatives given :
In

Δ P Q R

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and PT

⊥

QR then

∠ T P S

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Q. The internal bisectors of

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For the ΔPQR,PA is the angle bisector of ∠P, then AR=

The correct option is B QR2 Here, PA is the angle bisector of ∠P. In ΔPQA and ΔPRA, PQ=PR ∠QPA=∠RPA PA is common ΔPQA≅ΔPRA. ∴ The corresponding side lengths and angles will be equal for both the triangles. ⇒QA=RA ⇒2×QA=QR⇒QA=QR2 Or AR=QR2

For the $Δ P Q R, P A$ is the angle bisector of $∠ P$ , then $A R =$