Given: lp=np
ml=mn
prove: lq=qn

The Proof is below.

Step-by-step explanation:

Given:

To Prove:

Proof:

In  ΔLPM  and ΔNPM  

 ……….{Given}

 ……….{Given}

 ……….{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  

 ……….{Given}

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

 ……….{Reflexive Property}

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

∴ ...{Corresponding parts of congruent triangles (c.p.c.t).}.....Proved

12cm

the answer is d