In the given figure, l $∥$ m and M is the mid-point of the line segment AB. Which of the following options are correct?

M C = D M

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D M = M B

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A M = M C

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D M = A M

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Solution

The correct option is A $M C = D M$
In $Δ A M C$ and $Δ B M D$ , we have,
$∠ 1 = ∠ 3$ [alternate angles as l $∥$ m ]
$∠ 2 = ∠ 4$ [vertically opposite angles]
AM = BM [M is the mid-point of AB]

We see that two angles and the included side of $△ A M C$ are equal to two angles and the included side of $△ B M D$ .
$∴ Δ A M C ≅ Δ B M D$ [by ASA congruence rule]
$⟹$ CM = DM [CPCT]
Hence, M is also the mid-point of CD.

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Similar questions

In the given figure, $l ∥ m$ and $M$ is the mid-point of the line segment $A B .$ Which of the following options is/are correct?

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Q. Let

A (a, b)

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M_{1}

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M_{2}

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Question 77

State whether the statement is True or False.

If M is the mid-point of a line segment AB, then we can say that AM and MB are congruent.

AB is a line segment and M is its mid-point. Semi-circles are drawn with AM, MB and AB as diameters on the same side of AB. A circle is drawn to touch all the three semi-circles. Its radius is:

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In the given figure, l ∥ m and M is the mid-point of the line segment AB. Which of the following options are correct?

In the given figure, l $∥$ m and M is the mid-point of the line segment AB. Which of the following options are correct?