Question:
In a ΔABC, ∠A = 50°, ∠B = 60° and ∠C = 70°. Find the measures of the angles of the triangle formed by joining the mid-points of the sides of this triangle.
Solution:
In ΔABC,
D and E are mid points of AB and BC.
By Mid point theorem,
DE ∥ AC, DE = (1/2) AC
F is the midpoint of AC
Then, DE = (1/2) AC = CF
In a Quadrilateral DECF
DE ∥ AC, DE = CF
Hence DECF is a parallelogram.
∴ ∠C = ∠D = 70° [Opposite sides of a parallelogram]
Similarly
BEFD is a parallelogram, ∠B = ∠F = 60°
ADEF is a parallelogram, ∠A = ∠E = 50°
∴ Angles of ΔDEF are
∠D = 70°, ∠E = 50°, ∠F = 60°
