In the given figure, ﺎ ‖ m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points at ﺎ and m respectively.

Question

In the given figure, &#xFE8E; &#x2016; m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points at &#xFE8E; and m respectively.

Philoid · Accepted Answer

Here it is given that l ‖ m ie. AC ||DB.

Also given that AM = MB

Now in ∆AMC and ∆BMD,

∠CAM = ∠DBM … Alternate angles

AM = MB

∠AMC = ∠BMD … vertically opposite angles

Hence, ∆AMC ≅ ∆BMD … by ASA property of congruency

∴ CM = MD …cpct

Hence proved that M is also the midpoint of any line segment CD having its end points atﺎ and m respectively.

In the given figure, ﺎ‖m and M is the midpoint of AB. Prove that M is also the midpoint of any line segment CD having its end points atﺎ and m respectively.