Mathematics
In the given figure, M is the mid-point of AB and CD. Prove that CA = BD and CA || BD.
Triangles
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Answer
Given,
M is the mid-point of AB and CD.
Thus, MC = MD and MB = MA
In △MAC and △MBD,
⇒ MA = MB [Proved above]
⇒ MC = MD [Proved above]
⇒ ∠CMA = ∠BMD [Vertically opposite angles are equal]
∴ △MAC ≅ △MBD (By S.A.S. axiom)
⇒ CA = BD [Corresponding part of congruent triangles are equal.]
⇒ ∠CAM = ∠DBM [Corresponding part of congruent triangles are equal.]
Since, ∠CAM and ∠DBM are alternate angles and since they are equal,
∴ CA || BD
Hence, proved that CA = BD and CA || BD.
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