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Alja [10]
2 years ago
5

Given: LP=NP ML=MN Prove: LQ=QN

Mathematics
1 answer:
julsineya [31]2 years ago
4 0

Answer:

The Proof is below.

Step-by-step explanation:

Given:

\overline {LP} \cong \overline{NP}

\overline {ML} \cong \overline{MN}

To Prove:

\overline {LQ} \cong \overline{QN}

Proof:

In  ΔLPM  and ΔNPM  

\overline {LP} \cong \overline{NP}  ……….{Given}

\overline {ML} \cong \overline{MN}  ……….{Given}

\overline {LP} \cong \overline{NP}  ……….{Reflexive Property}

ΔLPM ≅ ΔNPM      ….{ By Side-Side-Side congruence test}

∴ ∠LMP ≅ ∠NMP  ...{Corresponding parts of congruent triangles (c.p.c.t).}.....( 1 )

Now In ΔLMQ  and ΔNMQ  

\overline {ML} \cong \overline{MN}  ……….{Given}

∠LMQ ≅ ∠NMQ                                 ..........{From 1 above}

\overline {MQ} \cong \overline{MQ}  ……….{Reflexive Property}

ΔLMQ ≅ ΔNMQ         ....{ By Side-Angle-Side Congruence test}

∴ \overline {LQ} \cong \overline{QN} ...{Corresponding parts of congruent triangles (c.p.c.t).}.....Proved

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