Question

AB and CD bicect each other at K.
Prove That AC=BD.​

Answer 1

Answer:

Step-by-step explanation:

given: k is mid point of both AB and CD

to prove: AC=BD

Proof: in triangle AKC and triangle BDK

            AK=BK           {because k is mid point of AB}

            CK=DK           {because k is mid point of CD}

angle AKC=angle BKD           {vertically opposite angles}

therefore triangle AKC congruent to triangle BDK

         BY C.P.C.T  AC=BD

                                                          HENCE PROVED

Answer 2

By the concept of congruency we solving this question.

given:

AB and CD bisect each other

Now,

Join AC and BD so that they form two triangles.

In ∆ ACK and ∆ KBD.

AK = KB ( AB & CD bisect each other )

CK = KD ( AB &CD bisect each other )

/_ CKA = /_ DKA (vertically opposite angles )

Here,

we have two sides and one angle between them equal in both the angles.

Hence,

∆ ACK ≈ ∆ DKB .......(SAS)

Therefore,

AC = BD .......( CPCT )

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