Question

A,B,C and D are collinear points . if AC=BD, then prove thatAB=CD

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Answer 1

Step-by-step explanation:

ABCD are collinear so AB+BC+CD=AD,

AC=AB+BC,

AC+CD=AD,AC=AD-CD

BC+CD=BD=AD-AB

AC=BD,given

AD-CD=AD-AB

Hence,AB=CD

Answer 2

Answer  :

Given :  AC = BD

To Prove : AB = CD

Solution :

AC = BD …………. (1)

#Refer the attachment for better understanding.

From figure,

AC = AB + BC …………. (2)

&  

BD = BC + CD …………. (3)

Substituting for BD and AC from eq. (2) and (3) in eq. (1),

Then we get :

AB + BC = BC + CD

AB = CD

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