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 L AC
(iii) CM = MA = 1/2AB
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Answer:
R.E.F. Image.
In △ABC,
(1) M is the mid point of AB and
MD∥BC
D is the mid point of AC
(2) As MD∥BC &
AC is transversal
∠MDC+∠BCD=180
∘
∠MDC+90
∘
=180
∘
⇒∠MDC=90
∘
⇒MD⊥AC
(3) In △AMD and △CMD
AD=CD
∠ADM=∠CDM
DM=DM
△AMD≅△CMD
AM=CM⇒AM=
2
1
AB⇒CM=AM=
2
1
AB
Step-by-step explanation:
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sonishourya498:
I did not understand please write properly
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