Question

In the triangle ABC , right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to point D such that DM =CM. Point D is joined to the point (see the Figure). Show that:
(i)∆AMC=~ ∆BMD
(ii) angle DBC is a right angle.
(iii) ∆DBC=~∆ACB
(iv) CM =1/2 AB​

Answer 1

Answer:

i- In ∆ AMC and ∆ BMD,

They are vertically opposite ANGLES.

AC=BD ( By CPCT).

ii- DBC is a Right angle because <1/2 of DBM & MBC . they are congruent , (BY CPCT )