Question

24
In the given figure, LM = MN, QM = MR, ML 1PQ and
MN I PR Prove that PQ = PR.​

Answer 1

Step-by-step explanation:

In triangle LMQ and triangle NMR

QM = RM (given)

LM = NM (given)

angle QLM = angle RNM (90°)

Hence,

triangle LMQ is equivalent to triangle NMR (by RHS)

Hence,

LQ = NR (by CPCT). -(1)

In triangle PLM and triangle PNM

LM = NM (given)

PM = PM (common)

angle PLM = angle PNM (90°)

Hence,

triangle PLM is equivalent to triangle PNM (by RHS)

Hence,

PL = PN (by CPCT). -(2)

Adding 1 and 2

LQ+PL = NM+PN

Hence PQ = PM

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Answer 2

Step-by-step explanation:

in ∆pqm and ∆prm

pm = pm (common side)

qm = mr ( given )

pmq = pmr ( angle between two equal sides is

equal )

therefore

∆pqm is congruent ∆prm ( sas congruency rule)

pq = pr ( cpct )

hence proved

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