Question

A diagonal of a parallelogram divides it into two congruent
(a) Squares
(b) Parallelograms
(c) Triangles
(d) Rectangles​

Answer 1

Answer:

A diagonal of a parallelogram divides it into 2 congruent triangles

Answer 2

$\green{\underline\bold{Answer :-}}$

A diagonal of a parallelogram divides it into two congruent

(C) Triangles.

✯ Explanation:

$\boxed{ \sf \blue{ Given, }}$

Let ABCD be a parallelogram with AC as its diagonal.

$\red{\underline\bold{To\:Prove,}}$

A diagonal of a parallelogram divides it into two congruent triangles.

i.e ΔABC ≅ ΔADC

$\boxed{ \sf \pink{ Proof, }}$

✏ We know that,

The opposite sides of a parallelogram are parallel.

So from the diagram,

✏ AB ∥ DC and AD ∥ BC

$\green{\underline\bold{Now,\:}}$

Since,

✏ AB ∥ DC and AC is the transversal

∴ ∠BAC = ∠DCA ( ∵ Alternate angles ) ────────────── (1)

And,

✏ AD ∥ BC and AC is the transversal

∴ ∠DAC = ∠BCA ( ∵ Alternate angles )

────────────── (2)

$\boxed{ \sf \blue{ Now\:in\:ΔABC \:and\:ΔADC, }}$

$\green{\underline\bold{From\:1,}}$

• ∠BAC = ∠DCA

$\green{\underline\bold{From\:2,}}$

• ∠DAC = ∠BCA
• AC = AC ( Common )

Therefore,

✏ ΔABC ≅ ΔADC

✏(By ASA congruency rule.)

$\red{\underline\bold{Hence,\:proved.}}$

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