Question

Geometric proofs of segments

Again..
Given: B is the midpoint of AC
C is the midpoint of BD
Prove: AD=3AB

This one hurts to look at

Answer 1

The proof is shown below.

Explanation:

Given: B is mid point of AC and C is mid-point of BD.

To prove: AD=3AB

It is given that B is mid-point of AC.

⇒ AB = BC ...(1)

Also, C is mid-point of BD.

⇒ BC = CD ...(2)

From (1) and (2),

AB = BC = CD

Now, AD = AB + BC + CD

⇒ AD = AB + AB + AB (∵ AB = BC = CD )

Hence proved.