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.)