ABC is a triangle right angled at C. A line through the mid point of hypothesis AB and parallel to BC intersects AC at D. Show that
i) D is the mid point of AC
ii) MD is perpendicular to AC
iii) CM=MA=½AB
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Answer:
In ∆ABC, we have
M is the midpoint of AB and MD||BC
D is the midpoint of AC {by converse of midpoint theorem}
Now
MP||BC
<MDC+<BCD=180°
<MDC+90°=180°
<MDC=90°
Thus;MD perpendicular AC
Join MC
In ∆MDA and ∆MDC we have
DA=DC
<MDA=<CDM
MD=MD
∆MDA~∆MDC {S.A.S}
And so MA=MC
Now M is the midpoint of AB
MA=MC=1/2AB
Step-by-step explanation:
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