In equilateral δabc, ad, be, and cf are medians. if bc = 12, then do =
a) 2 square root 3
b) 3
c) 6
d) 6 square root 3

Option A) 2 square root 3

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal angles (60 degrees each)

The triangle BOD is a right triangle

we have

<OBD=(60°/2)=30°

BD=12/2=6 units

tan(<OBD)=DO/BD

tan(30°)=DO/6

DO=6*tan(30°)

DO=2√3 units

∠3=140°

Step-by-step explanation:

∠4 = 40°

∠3 + ∠4 = 180° (co-exterior angles are equal)

∠3 + 40° = 180°

∠3 = 180° - 40°

∠3 = 140°

∠2 = ∠4 = 40° (corresponding angles)

∠3 + ∠2 = 180° (linear pair)

∠3 + 40° = 180°

∠3 = 180° - 40°

∠3 = 140°

hope you understood