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# 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

**☛ Check: **Class 9 Maths NCERT Solutions Chapter 5

**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.

**☛ Related Questions:**

- In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
- In Fig. 5.10, if AC = BD, then prove that AB = CD.
- Why is Axiom 5, in the list of Euclid’s axioms, considered a 'universal truth'? (Note that the question is not about the fifth postulate.)

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