In right triangle ABC, right angle is at C,M is the mid-point of hypotenuse AB,C is joined to M and produced to a point D such that DM=CM. Point D is joined to point B. Show that: △AMC≅△BMD
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Solution
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In right angled △ABC,
∠C=90∘,
M is the mid-point of AB i.e, AM=MB & DM=CM
In △AMC and △BMD,
AM=BM ------ (M is the mid-point)
∠CMA=∠DMB ------ (Vertically opposite angles)
CM=DM ------ (Given)
∴△AMC≅△BMD, by SAS Postulate
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