Question 4If a point C lies between two points A and B such that AC = BC, then prove that AC = 12\dfrac{1}{2}21 AB. Explain by drawing the figure.

Question

Question 4If a point C lies between two points A and B such that AC = BC, then prove that AC = 12\dfrac{1}{2}21​ AB. Explain by drawing the figure.

Accepted Answer

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 = $\dfrac{1}{2}$ AB

⇒ Hence, proved that AC = $\dfrac{1}{2}$ AB.

Introduction to Euclid's Geometry — Question 4