In a triangle ABC, angle A=40o,, angle B=80o, angle C=60o. Find the measures of the angles of the angles of the triangles formed by joining the midpoints of this triangle.
Please answer fast my worksheet is due on monday!!
Here is the answer to your query.
Given : ABC is a triangle with ∠A = 40°, ∠B = 80°, ∠C = 60°.
Let D, E, F be the mid points of side BC, AC, AB respectively.
Now according to mid point theorem, The line segments joining the mid points of the sides of a triangle is parallel to the third side of triangle.
⇒ FE // BC
⇒ FE // BD and FE // DC ..... (1)
ED // AB
⇒ ED // AF and ED // FB ..... (2)
FD // AC
⇒ FD // AE and FD // EC ..... (3)
from (1), (2) and (3) we can conclude that
AFDE, BFED, DFEC are parallelogram.
Also opposite angles of a parallelogram are equal
⇒ ∠FAE = ∠FDE = 40°
⇒ ∠FBD = ∠FED = 80°
⇒ ∠DCE = ∠DFE = 60°
∴ In ΔDEF
∠D = 40°, ∠E = 80° and ∠F = 60°