Answer:
The Proof is below.
Step-by-step explanation:
Given:
[tex]\overline {LP} \cong \overline{NP}[/tex]
[tex]\overline {ML} \cong \overline{MN}[/tex]
To Prove:
[tex]\overline {LQ} \cong \overline{QN}[/tex]
Proof:
In ΔLPM and ΔNPM
[tex]\overline {LP} \cong \overline{NP}[/tex] ……….{Given}
[tex]\overline {ML} \cong \overline{MN}[/tex] ……….{Given}
[tex]\overline {LP} \cong \overline{NP}[/tex] ……….{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
[tex]\overline {ML} \cong \overline{MN}[/tex] ……….{Given}
∠LMQ ≅ ∠NMQ ..........{From 1 above}
[tex]\overline {MQ} \cong \overline{MQ}[/tex] ……….{Reflexive Property}
ΔLMQ ≅ ΔNMQ ....{ By Side-Angle-Side Congruence test}
∴ [tex]\overline {LQ} \cong \overline{QN}[/tex] ...{Corresponding parts of congruent triangles (c.p.c.t).}.....Proved
