# If a point C lies between two points A and B such that AC = BC, then prove that AC = 1/2 AB. Explain by drawing the figure.

**Solution:**

According to Euclid's axioms, we know that when equals are added to equals, the wholes are equal.

Given: AC = BC

Adding AC on both sides, we get

⇒ AC + AC = BC + AC (BC + AC coincides with AB)

⇒ 2 AC = AB

⇒ AC = 1/2 AB

**Video Solution:**

## If a point C lies between two points A and B such that AC = BC, then prove that AC = 1/2 AB. Explain by drawing the figure.

### NCERT Solutions Class 9 Maths - Chapter 5 Exercise 5.1 Question 4:

**Summary:**

Hence, we have proved that if a point C lies between two points A and B such that AC = BC, then AC = 1/2 AB using Euclid's axiom.