Question

8. In right triangle ABC, right angled at C. Mis
the mid-point of hypotenuse ABC 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) A AMC = A BMD
(ii) Z DBC is a right angle.
(ii) A DBC = A ACB
Fig. 7.23
(iv) CM =
AB​

Answer 1

Step-by-step explanation:

Given,

AM=BM(M is the mid point)

Angle BMD=Angle AMC (Vertically opposite angle)

DM=CM(gn)

By SAS Congruency rule,

i)Triangle AMC is congruent to triangle BMD

ii)

Angle DBC+90 = 180 (co interior angle)

Angle DBC=90

iii)

Triangle DBC is congruent to triangle ACB

By SAS Congruency rule,

Triangle DBC is congruent to ACB

iv)

CM=1/2AB

AB = 2cm

2cm =AB

CM=AB/2

CM=1/2AB