Question

If a point C lies between two points A and B such that AC = BC, then prove that AC = \(\frac{1}{2}\)AB. Explain by drawing the figure.

Answer 1

Data: C lies between A and B such that AC = BC. 

To Prove: AC = \(\frac{1}{2}\)AB 

Proof : In this figure AC = BC. 

Adding AC on both sides, 

AC + AC = BC + AC (equals are added to equals) 

2AC = BC + AC 

2AC = AB (∵ BC + AC = AB) 

∴ AC = AB.