Question

Line segment AB&CD intersect at M if AC is parallel to DB & M is midpoint of AB. Prove that M is midpoint of CD

Answer 1

If the line segment AB & CD intersect at M and AC is parallel to DB & M is midpoint of AB, the it is proved that M is a midpoint of CD.

Step-by-step explanation:

It is given that,

AC // DB

Line AB intersect line CD at point M

M is the midpoint of AB i.e., AM = BM …… (i)

Now, consider ΔAMC and ΔBMD, we have

∠AMC = ∠BMD ....... [vertically opposite angles]

∠CAM = ∠DBM ....... [alternate angles]

∴ By AA similarity, ΔAMC ~ ΔBMD

We know that the corresponding sides of similar triangles are proportional to each other.

∴ $\frac{AM}{BM} = \frac{CM}{DM}$

from (i) we have AM = BM

⇒ 1 = $\frac{CM}{DM}$

⇒ CM = DM

∴ M is a mid point of the line segment CD

Hence proved

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