Question

In a ABC,
A = 40°, B = 80° and C = 60°. Find
the measurement of the angles of the triangle formed by
joining the mid-points of the sides of this triangle.​

Answer 1

Answer:

40°, 80° and 60°

Step-by-step explanation:

In ΔABC, let's name mid point of AB as D, mid point of BC as E and Mid point of CA as F.

Now between ΔDBE and ΔABC:

BD:AB = 1:2 [∵ D is mid point of AB]

Similarly, BE:BC = 1:2

Since the ratios of the sides are equal, then these triangles are similar.

∴ DE is parallel to AC

Similarly, DF is parallel to BC and EF is parallel to BA.

∴ ADEF is a parallelogram.

∠EDF = ∠DFA [∵ they are alternate interior angles]

∠DFA = ∠ECF [∵ they are corresponding angles]

∴ ∠EDF = ∠BCA = 60°

Similarly, ∠DEF = ∠BAC = 40° and ∠EFD = ∠ABC = 80°