Question

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 figure). Show that (i) ∆AMC ≅ ∆BMD (ii) ∠DBC is a right angle (iii) ∆DBC ≅ ∆ACB
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Answer 1

Step-by-step explanation:

i) let, take ∆AMC and ∆BMD-----

AM=BM (M is the mid-point)

<AMC=<BMD (vertically opposite)

CM=DM (Given)

thus, ∆AMC cong ∆BMD by SAS Congruency.

also, <CAB=<BDC and AC=BD by c.p.c.t.

now, in ∆ ACB and ∆ DBC-----

AC=BD(proved)

<CAB=<BDC(proved)

BC=BC(common)

thus, ∆ACB cong. ∆DBC by SAS Congruency.---(1)

also, <ACB = <DBC by C.P.C.T.

ii) <DBC=90°

iii) From (1).....

May this help uuuu.

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