Question

C is the mid point of the segment AB.P and Q are mid point of segments AC and BC respectively.Prove that AP=BQ=1/4AB

Answer 1

It is your answer..........

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

C is midpoint of AB

$\implies AC =\frac{1}{2}AB$

Also, P is midpoint of AC

$\implies AP =\frac{1}{2}AC\\\\\implies 2AP=AC\\\\\implies 2AP=\frac{1}{2}AB\\\\\implies AP=\frac{1}{4}AB.........(1)$

Now, C is midpoint of AB

$\implies BC =\frac{1}{2}AB$

Also, Q is midpoint of BC

$\implies BQ=\frac{1}{2}BC\\\\\implies 2BQ=BC\\\\\implies 2BQ=\frac{1}{2}AB\\\\\implies BQ=\frac{1}{4}AB.........(2)$

$\text{From equation (1) and equation (2), We get, }\\\\AP=BQ=\frac{1}{4}AB$

Hence Proved.