Question

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC

intersects AC at D. Show that

(i) D is the mid-point of AC

(ii) MD 丄 AC

(iii) CM = MA= ½ AB plzz answer in short​

Answer 1

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Answer 2

Answer:

Midpoint theorem has to be used...

angle C= angle D (corresonding angles)

Join CM

(i) Converse of mid point theorem

(ii)MD⊥AC as ∠D=90 and DM║CB

(iii)ΔADM≅ΔCDM

∴AD=CD

∠ADM=∠CDM=90 (linear pair)

DM=DM (Common)

∴Congruent by SAS

AM=CM by CPCT

AM=1/2AB because M is midpoint

∴AM=CM=1/2 AB