Question

1. In the adjoining firgure ,show that AC =BD if AB= CD​

Answer 1

Step-by-step explanation:

Given,

AC=BD ... (i)

AC=AB+BC ……(ii) (Point B lies between A and C)

BD=BC+CD … (iii) (Point C lies between B and D)

Now,

substituting (ii) and (iii) in (i), we get

⇒AB+BC=BC+CD

⇒AB+BC–BC=CD

⇒AB=CD

Hence, AB=CD.

Answer 2

Answer:

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