Question

in the adjoining figure it is given that l m is equal to m n u m is equal to M R M L perpendicular PQ and MN perpendicular PR prove that PQ is equal to PR

Answer 1

Ello There!

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The question youve written is a bit unclear, Ive written it again, the figure is attached as well :D

Question: In figure, it is given that LM=MN, QM=MR, ML ⊥ PQ and MN ⊥ PR. Prove that PQ=PR.

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Given

PQR is a triangle.

LM = MN

QM = MR

ML ⊥ PQ

MN ⊥ PR.

To Prove

PQ = PR

Proof

In ΔLMQ and ΔNMR,

QM = MR (given)

LM = MN (given)

∠MLQ = ∠MNR = 90° (MR and ML are perpendicular bisectors)

∴ ΔLMQ ≅ ΔNMR by RHS congruency.

⇒ ∠Q = ∠R (CPCT)

In ΔPQR

∠Q = ∠R (proved)

∴ PQ = PR

(Sides opposite to equal angles are equal)

Hence Proved!

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Thank You!

@tomboyish44