**Prove that: **A Diagonal of a parallelogram divides it into two congruent triangles.

its vry simple

see

there can b two pairs of alternae interior angles equal as it is a parallegram.

and one side is common

there fore the two triangles are congruent by ASA criteria.

therefore a diagonal of a parallelogram divides it into two congruent triangles

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in IIgm opp. sides are equal so in a llgm ABCD , AB = CD and BC= DA.

So , now draw a diagonal AC inside the llgm then,

In triangle ABC and ADC

AB=AD [GIVEN]

AC = AC [COMMON]

BC=DA [GIVEN]

SO Triangle ABC and ADC are congruent by SSS congruence rule

# HENCE PROVED..... THANK YOU...

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abcd is a parallelogram and ac is the diagonal .

so in triangle abc and triangle cda

ab = cd (as they are opposite sides of a parallelogram)

bc = da (opposite sides of a parallelogram)

ac = ac (common)

therefore triangle abc is congruent to triangle cda

area of congruent triangles are equal

so area of abc is equal to area of cda

so in triangle abc and triangle cda

ab = cd (as they are opposite sides of a parallelogram)

bc = da (opposite sides of a parallelogram)

ac = ac (common)

therefore triangle abc is congruent to triangle cda

area of congruent triangles are equal

so area of abc is equal to area of cda

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in IIgm opp. sides are equal so in a llgm ABCD , AB = CD and BC= DA.

So , now draw a diagonal AC inside the llgm then,

In triangle ABC and ADC

AB=AD [GIVEN]

AC = AC [COMMON]

BC=DA [GIVEN]

SO Triangle ABC and ADC are congruent by SSS congruence rule

# HENCE PROVED..... THANK YOU...

So , now draw a diagonal AC inside the llgm then,

In triangle ABC and ADC

AB=AD [GIVEN]

AC = AC [COMMON]

BC=DA [GIVEN]

SO Triangle ABC and ADC are congruent by SSS congruence rule

# HENCE PROVED..... THANK YOU...

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Proving theorom

Given:ABCD is a parallelogram.

Diagonal AC is drawn.

RTP:Triangle ABC and triangle ACD are congruent

Proof:Consider triangles ABC and ACD

AB=CD(opposite sides of parallelogram)

AD=BC(as given above)

AC=AC(common)

Therefore triangles ABC and ACD are congruent

Hence proved

Hope it helped

Given:ABCD is a parallelogram.

Diagonal AC is drawn.

RTP:Triangle ABC and triangle ACD are congruent

Proof:Consider triangles ABC and ACD

AB=CD(opposite sides of parallelogram)

AD=BC(as given above)

AC=AC(common)

Therefore triangles ABC and ACD are congruent

Hence proved

Hope it helped

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