In fig., if AC = BD, then prove that AB = CD - Vidyadip

Question

In fig., if AC = BD, then prove that AB = CD

✓

Answer

AC = BD . . . . [Given] . . . (1)
AC = AB + BC . . . . [Point B lies between A and C] . . . . (2)
BD = BC + CD . . . . [Point C lies between B and D] . . . . (3)
Substituting (2) and (3) in (1), we get
AB + BC = BC + CD
$\Rightarrow A B=C D \ldots .$ [Subtracting equals from equals]

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Model Paper 1→Model Paper 1 — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

If $x=\frac{1}{2}$ is a zero of the polynomial $f(x)=8 x^3+a x^2-4 x+2$, find the value of $a$.

If the supplement of an angle is three times its complement, find the angle.

Factorise:
$a^3+8 b^3+64 c^3-24 a b c$

Three angles of a quadrilateral are $75^\circ , 90^\circ $ and $75^\circ $. Find the measure of the fourth angle.

Find two rational and two irrrational numbers between $0.5$ and $0.55.$

Factorise:
$10 x^2-9 x-7$

The average weight of $10$ oarsmen in a boat is increased by $1.5\ kg$ when one of the crew who weighs $58\ kg$ is replaced by a new. Find the weight of the new man.

Verify $x = - \frac{1}{2}$ are zeroes of the polynomial $p\left( x \right) = 2x + 1$

Multiply: $3\sqrt{5}$ by $2\sqrt{5}$

Factorise:
$125 a^3+b^3+64 c^3-60 a b c$