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.

8 0

2 years ago

Serious answers only please !! 20 points as well as brainliest for correct answer!!

Gre4nikov [31]

Answer:

Measure of angle A = 55°.

Step-by-step explanation:

From the picture attached,

$\frac{AC}{LN}=\frac{BC}{LM}$

$\frac{10}{5}=\frac{8}{4}$

2 = 2

Corresponding sides of the given triangles ΔACB and ΔNLM are proportional.

Therefore, ΔACB ~ ΔNLM.

m∠A = 180° - (90° + 35°) [By triangle sum theorem]

= 180° - 125°

= 55°

Measure of angle A is 55°.

8 0

3 years ago

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