# 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

**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.