Question

Find the measures of the angles of the triangle formed by joining the midpoints of the sides of the triangle

Answer 1

Step-by-step explanation:

Suppose we have a triangle ABC such that, <A=40, <B=80 and <C= 60 deg.

The midpoints of BC is D, AC is E and AB is F. Join DEF.

Now we have AEDF as a parallelogram. <EDF opposite <A = 40 deg.

We have BDEF as a parallelogram. <DEF opposite <B = 80 deg.

We have CDFE as a parallelogram. <DFE opposite <C = 60 deg.

Conclusion: The angles formed by joining the midpoints of the sides of a triangle will be the same as the angle opposite them in the original, main triangle.