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Quadrilaterals | Quadrilaterals - Exercise 8.4

Question 6

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

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Let the parallelogram be = ABCD

Diagonal AC bisect ∠A.

∠CAB = ∠CAD

Now,

AB||CD and AC is a transversal.

∠CAB = ∠ACD

Again, AD||BC and AC is a transversal.

∠DAC = ∠ACB

Now,

∠A = ∠C

½ ∠A = ½ ∠C

∠DAC = ∠DCA

AD = CD

But, AB = CD and AD = BC (Opposite sides of parallelograms)

AB = BC = CD = AD

Thus, ABCD is a rhombus.

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Our top 5% students will be awarded a special scholarship to Lido.

subject-cta

Question 6

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Let the parallelogram be = ABCD

Diagonal AC bisect ∠A.

∠CAB = ∠CAD

Now,

AB||CD and AC is a transversal.

∠CAB = ∠ACD

Again, AD||BC and AC is a transversal.

∠DAC = ∠ACB

Now,

∠A = ∠C

½ ∠A = ½ ∠C

∠DAC = ∠DCA

AD = CD

But, AB = CD and AD = BC (Opposite sides of parallelograms)

AB = BC = CD = AD

Thus, ABCD is a rhombus.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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