Question

ab and CD bisect each other at K prove that AC is equals to BD

Answer 1

Hey dear here is your answer!!!!!

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We would be using the concept of Congruency to solve this question.

Firstly, let's note down the information provided to us:-

AB and CD bisect each other.

Now, Join AC and BD so that they form two triangles.

In Triangles ACK and KBD:-

AK = KB ( AB and CD bisect each other)

CK = KD ( AB and CD bisect each other)

∠CKA = ∠DKB (Vertically Opposite Angles)

Here, we have 2 sides and and one angle between them equal in both the triangles.

Hence, ΔACK ≅ ΔDKB    ...(SAS)

Therefore, AC = BD     ...(CPCT)

❣️⭐ Hope it helps you dear...⭐⭐❣️❣️

Answer 2

Ello There!

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Question: AB and CD bisect each other at K. Prove that AC = BD

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Pre-requisite Knowledge

• SSS congruency rule
• SAS congruency rule
• ASA congruency rule
• AAS congruency rule
• RHS congruency rule
• Corresponding parts of congruent triangles are equal.

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Answer

Given,

AB bisects CD

∴ AK = BK , DK = CK

To Prove

AC = BD

Proof

In ΔAKC and ΔBKD

AK = BK (given)

∠AKC = ∠DKB (Vertically opposite angles)

CK = DK (given)

∴ Δ AKC ≅ ΔBKD by SAS congruency

(Crucial to mention through what congruency the triangles are congruent)

⇒ AB = CD (CPCT)

Hence, Proved!

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Hope It Helps!