Question

In figure, it is given that LM=MN,QM=MR,ML is perpendicular to PQ and MN is perpendicular to PR. Prove that PQ=PR.

Answer 1

Hope it help you dear.

Answer 2

Answer:

Step-by-step explanation:

Two lines exist said to be perpendicular to each other when they intersect each other at 90 degrees or right angles.

Given,

LM=MN,QM=MR,ML exist perpendicular to PQ and MN exist perpendicular to PR.

To prove, PQ=PR.

In $\triangle \mathrm{QLM}$ and $\triangle \mathrm{RNM}$

$\mathrm{QM}=\mathrm{MR}$

$\mathrm{LM}=\mathrm{MN}$

$\angle \mathrm{QLM}=\angle \mathrm{RNM}=90^{\circ}$

Therefore, $\triangle \mathrm{QLM} \cong \triangle \mathrm{RNM}$.... (RHS criteria)

Hence, QL = RN .........(i)

Join PM

In$\triangle \mathrm{PLM}$ and$\triangle \mathrm{PNM}$ and

PM = PM. .. .common)

$\mathrm{LM}=\mathrm{MN}$

$\angle \mathrm{PLM}=\angle \mathrm{PNM}=90^{\circ}$

Therefore, $\triangle \mathrm{PLM} \cong \triangle \mathrm{PNM} \quad$...(RHS criteria)

Hence, PL = PN ..........(ii)

From (i) and (ii)

PQ=PR.

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