Question

Question 8
In the figure, $l\parallel m$ and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points of l and m, respectively.

Answer 1

Given: In the figure, $l\parallel m$ and M is the mid-point of a line segment AB i.e., AM = BM.
To prove: CM = DM.

Proof:
$\angle BAC=\angle ABD$ [alternate interior angles]
$\angle AMC=\angle BMD$ [vertically opposite angles]

In $\Delta AMC$ and $\Delta BMD,$
$\angle BAC=\angle ABD$ [proved above]
AM =BM [given]
and $\angle AMC=\angle BMD$ [proved above]
$\therefore \Delta AMC\cong \Delta BMD$ [by ASA congruence rule]
$\Rightarrow MC=MD$ [by CPCT]