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slavikrds [6]
3 years ago
8

In ΔABC, point M is the midpoint of side AB and point D is the midpoint of segment MC. Prove that the area of ΔADC= the area of

ΔBMD
Mathematics
1 answer:
Anna11 [10]3 years ago
8 0
A line segment from a vertex to the midpoint of the opposite side is a "median". A median divides the area of the triangle in half, as it divides the base in half without changing the altitude.
AAMC is half AABC. AADC is half AAMC, so is 1/4 of AABC. (By the formula for area of a triangle.)
ABMC is half AABC. ABMD is half ABMC, so is 1/4 of AABC. (By the formula for area of a triangle.)
Then, AADC = 1/4 AABC = ABMC, so AADC = ABMC by the transitive property of equality.
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