Question

in triannd triangle pqr,angle n=angle q=90 degree,MN=gle mnt aPQ and NT = QR.which of the following property can be used to prove congruence of triangle MNO and triangle PQR?

Answer 1

Answer:

So, by SSS congruence criterion, we obtain

ΔNML≅ΔLPN

⇒∠MNL=∠PLN and ∠MLN=∠LNP

⇒∠MNL=∠LNP=∠PLM=∠MLN

⇒∠PNM=∠PLM

∴LN=MN

Step-by-step explanation:

Using mid-point theorem,

we have

MN∥PQ and MN=½ PQ⇒MN=PL

Similarly, we have

LM=PN

In triangles NML and LPN, we have

MN=PL

LM=PN

and, LN=NL

So, by SSS congruence criterion, we obtain

ΔNML≅ΔLPN

⇒∠MNL=∠PLN and ∠MLN=∠LNP

⇒∠MNL=∠LNP=∠PLM=∠MLN

⇒∠PNM=∠PLM

∴LN=MN