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# In Fig. 5.10, if AC = BD, then prove that AB = CD.

**Solution:**

According to Euclid's axioms, we know that when equals are subtracted from equals, the remainders are equal.

Given: AC = BD

Hence, AB + BC = BC + CD

[Since Point B lies between A and C; Point C lies between B and D]

Subtracting BC from both sides,

⇒ AB + BC - BC = BC + CD - BC

⇒ AB = CD

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

**Video Solution:**

## In Fig. 5.10, if AC = BD, then prove that AB = CD.

NCERT Solutions Class 9 Maths Chapter 5 Exercise 5.1 Question 6

**Summary:**

Hence, using Euclid's axioms, we have proved that if in the given figure AC = BD, then AB = CD.

**☛ Related Questions:**

- 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.
- 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.
- 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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