Mathematics
In the given figure, the line segments AB and CD intersect at a point M in such a way that AM = MD and CM = MB. Prove that, AC = BD but AC may not be parallel to BD.
Triangles
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Answer
In △MAC and △MDB,
⇒ AM = MD [Given]
⇒ CM = MB [Given]
⇒ ∠AMC = ∠DMB [Vertically opposite angles are equal]
∴ △MAC ≅ △MDB (By S.A.S axiom)
⇒ AC = BD [Corresponding parts of congruent triangles are equal.]
⇒ ∠MDB = ∠MAC [Corresponding parts of congruent triangles are equal.]
∴ ∠MDB ≠ ∠MCA
Thus, we cannot prove that AC // BD.
Hence, proved that AC = BD but AC may not be parallel to BD.
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