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 the figure). Show that:
⦁ ∆AMC ≅ ∆BMD (ii) ∆DBC is a right angle. (iii) ∆DBC ≅ ∆ACB (iv) CM = AB

Answer 1

Answer:

SHOULD'NT IT BE CD=AB???

in ΔAMC AND ΔBMD

AM=BM (GIVEN)

CM=DM(GIVEN)

∠AMC=∠BMD(VOA)

ΔAMC≅ΔBMD (SAS)

AC=DB (CPCT)

∠A=∠D(CPCT)

INΔABC AND ΔDCB

∠A=∠D (PROVED ABOVE)

AC=DB (PROVED ABOVE)

BC=CB (COMMON)

ΔABC≅ΔDCB(SAS)

AB=CD (CPCT)

Step-by-step explanation: