Question

In the Given figure,L and M are the liquid are the mid-points of AB and BC respectively.
(i) If AB =BC, prove that AL=MC
(ii) If BL =BM, prove that AB=BC

Answer 1

(i) according to the diagram

we know that $L$ is the midpoint of the line $AB$

so we get

$AL=BL=\frac{1}{2}AB................\left(1\right)$
we know that M is the midpoint of the line BC

so we get

$BM=MC=\frac{1}{2}BC...........\left(2\right)$
According to the question

it is given that

$AB=BC$
we can also write it as

$\frac{1}{2}AB=\frac{1}{2}BC$
according to equation (1) and (2)

we can write it as

$AL=MC$
(ii) According to the Diagram
we know that L is the midpoint of the line $AB$
so we get

$AL=BL=\frac{1}{2}AB$

The above equation can be written as

$2AL=2BL=AB........\left(3\right)$
we also know that M is the midpoint of the line BC

$BM=MC=\frac{1}{2}BC$
the above equation can be written as

$2BM=2MC=BC...........\left(4\right)$
according to question

it is given that

$BL=BM$
according to the equation (3) and (4)
we can write it as

$AB=BC$