Question

State whether the following statement is true or false.

In the figure, C in the mid-point of the segment AB, P and Q are mid-point of the segment AC and BC respectively. Then, $AP=BQ=\frac{1}{4}AB$.

• A. True
• B. False

Answer 1

The correct option is A True

In the figure, C is the mid-point of the segment AB.
AC =$\frac{1}{2}$AB .....(1)

AP =$\frac{1}{2}$AC .....(2)

From (1) and (2), we get

AP = $\frac{1}{2}$$\times \frac{1}{2}$AB = $\frac{1}{4}$AB.

Similarly, we have
BC=$\frac{1}{2}$AB and BQ=$\frac{1}{2}$BC.

BQ=$\frac{1}{2}\times$$\frac{1}{2}$AB = $\frac{1}{4}$AB.

Therefore, we have,
AP=BQ=$\frac{1}{4}$AB.