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

Question

slavikrds [6]

2 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] · Answer 1 · 2022-08-17T03:54:03+03:00

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.