Question

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

Answer 1

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