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State true or false.

In the figure given below, $A B C$ and $A B D$ and are two triangles on the base $A B$ are two triangles on the base . If line segment $C D$ . If line segment is bisected by $A B$ is bisected by at $O$ at , then $a r e a Δ A B C = a r e a Δ A B D .$ , then

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True

False

answer is A.

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Detailed Solution

Given a figure.
Question Image

A B C

and

A B D

are two triangles on the base

A B

.
The line segment

C D

is bisected by

A B

O

.
We have to show that

a r e a Δ A B C = a r e a Δ A B D .

.
So,

A O

is the median of

Δ A C D .

The median of the triangle divides it into triangles of equal areas.
We know that the median divides a triangle into

2

triangles of equal areas.
Therefore,

a r (Δ A O C) = a r (Δ A O D)

. . . . . . . (1)
And,

B O

is the median of

Δ B C D .

Therefore,

a r (Δ B O C) = a r (Δ B O D)

. . . . . . . (2)
Adding (1) and (2), we get,

a r (Δ A O C) + a r (Δ B O C) = a r (Δ A O D) + a r (Δ B O D)

⇒ a r (Δ A B C) = a r (Δ A D B)

Hence, the statement is true.
Hence, option 1 is correct.

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