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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

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

  
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