Question

Prove that "A diagonal of a 11 gm divides it intotwo congrent triangle".​

Answer 1

Step-by-step explanation:

opposite side of a parallelogram are equal and parallel.

In ||gm ABCD,

AB = CD

AC = BD

Let, suppose BC is a diagonal.

opposite angles are equal in ||gm,

CAB = CDB

ACD = ABD

Now, in triangle CAB and triangle BDC,

AB = CD

AC = BD

BC = BC ( Common side )

this implies,

triangle CAB =~ BDC by SSS property.

HENCE PROVED.

Answer 2

Let PQRS be the required ||gm. Let us construct a diagonal AC. Now, we have to prove that the two triangles formed are congruent.

In △ACD and △ACB,

1. AD = CB {Opposite sides of a ||gm are same}
2. AC = CA {Common side}
3. AB = CD {Opposite sides of a ||gm are same and ||}.

⇒△ACD ≅ △ACB (by S-S-S congruence criteria).

Hence, proved.

More:-

A given quadrilateral is a ||gm if:-

• Opposite sides are parallel.
• Opposite sides are same.
• Opposite angles are same.
• The diagonals bisect each other.