Question

ABCD is a rhombus show that angle AC bisects angle A as well as angle C and diagonal BD bisects Angle B as well as angle d

Answer 1

Ello There!

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Question: ABCD is a rhombus show that angle AC bisects angle A as well as angle C and diagonal BD bisects Angle B as well as angle D.

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Answer

Given,

ABCD is a rhombus.

Therefore all sides are equal.

To Prove

AC bisects ∠A and ∠C

BD bisects ∠B and ∠D

Proof

Part 1: Proof for AC bisects ∠A and ∠C

In ΔABC

AB = BC

∴ ∠2 = ∠4 (angles opposite to equal sides are equal)

AD ║BC  and AC is the transversal.

∠1 = ∠4 (Alternate interior angles)

∠2 = ∠4 (proved)

∴ ∠1 = ∠2

(things which are equal to the same thing are equal to one another)

⇒ AC bisects ∠A → 1

AB ║ DC and AC is the transversal.

∠3 = ∠4

But we have proved that ∠2 = ∠4

∴ ∠3 = ∠4

(things which are equal to the same thing are equal to one another)

⇒AC bisects ∠C → 2

From 1 and 2 we can tell that

AC bisects both ∠A and ∠C

Similarly we can prove that

BD bisects both ∠B and ∠D

Hence Proved!

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Thank You!

Answer 2

Answer:

hope it will help you