In right triangle ABC, right-angled 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 (see Fig. 7.23). Show that:
(i) ΔAMC ≅ ΔBMD
(ii) ∠DBC is a right angle.
(iii) ΔDBC ≅ ΔACB
(iv) CM = 1/2 AB
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Step-by-step explanation:
In triangle AMC and triangle BMD :
Since M is the mid point of AB
therefore AM = BM
CM = DM (given)
Angle AMC = Angle BMD (vertically opposite angles)
Therefore, Triangle AMD is congruent to Triangle BMD
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