# Ex.5.1 Q4 Introduction to Euclids Geometry Solution - NCERT Maths Class 9

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## Question

If a point \(C\) lies between two points \(A\) and \(B\) such that \(AC = BC\), then prove that

\(\begin{align}AC = \frac{1}{2}AB.\end{align}\) Explain by drawing the figure.

Video Solution

Introduction To Euclids Geometry

Ex 5.1 | Question 4

## Text Solution

**Reasoning:**

We are aware that when equals are added to equals, the wholes are equal.

**Steps:**

\[AC =BC\]

Adding \(AC\) on both sides, we get

\[\begin{align}&AC+AC=BC+AC \\ &2AC=AB \\\\& \left( \text{BC}\text{+}\text{AC}\,\,\text{coincides with}\text{AB} \right) \\&AC=\frac{1}{2}AB \\ \end{align}\]