Question

solve it please

Triangles​

Answer 1

Given :-

Two triangles ABC and PQR

AM and PN are respective median such that

AB = PQ

BC = QR

AM = PN

To prove:-

( I) Triangle ABM is congrent to Triangle PQN

(II) Triangle ABC is congrent to Triangle PQR

Prove :-

In traingles ABC and PQR

BC = QR ( Given )

so

1\2 BC = 1\2 QR

= BM = QN ( as AM and PN are medium)

In triangles ABM and PQN

AB = PQ ( Given )

BM = QN ( proved above )

AM = PN ( Given )

Therefore by SSS Congrency rule

Triangle ABM is congrent to Triangle PQN

so

Angle B = Angle Q ( C.P.C.T)

NOW

(II)

In triangles ABC and PQR

AB = PQ ( Given )

Angle B = Angle Q ( proved above )

BC = QR ( Given)

Therefore by SAS Congrency axiom

Triangle ABC is congrent to Triangle PQR

HENCE PROVED

We know :-

• A median of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex.

• There are basically four congruency rules that proves if two triangles are congruent

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side)