In the given figure- line - - line - and - is the mid-point of the line segment - Then- which of the following options is correct-

In Δ AMC and Δ BMD, we have: ∠ MAC=∠ MBD nbsp; [Alternate interior angles] ∠ AMC=∠ BMD nbsp; [Vertically nbsp;opposite nbsp;angles] AM = BM nbsp; [M ...

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Byju's Answer

Standard IX

Mathematics

ASA Criteria for Congruency

In the given ...

Question

In the given figure, line 𝑙 || line 𝑚 and 𝑀 is the mid-point of the line segment 𝐴𝐵. Then, which of the following options is correct?

C M = D M

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D M = B M

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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 $C M = D M$
In $Δ A M C$ and $Δ B M D$ , we have:
$∠ M A C = ∠ M B D$ [Alternate interior angles]
$∠ A M C = ∠ B M D$ [Vertically opposite angles]
$A M = B M$ [ $M$ is the mid-point of $A B$ ]

$∴ Δ A M C ≅ Δ B M D$ [by ASA congruence rule]
$⟹$ $C M = D M$ [CPCT]

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