in a triangle abc angle equals to 40 degree angle B equals to 80 degree and Angle C equals to 60 degree find the measurement of the angles of the Triangle formed by joining the midpoints of the sides of the triangle
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The measurements of angles of triangle formed by joining the mid points of the sides of the triangle ABC are 40°, 60° and 80°
Step-by-step explanation:
In a ΔABC, ∠A = 40°, ∠B = 80° and ∠C = 60°
Now mark mid point of each side of triangle ABC
D is mid point of AB, E is mid point of BC and F is mid point of AC
As shown in diagram in attachment.
D is mid point of AB and F is mid point of AC
DF parallel to BC, By mid point theorem of triangle.
Therefore, ∠ABC = ∠ADF = 80° ( ∵ DF || BC , corresponding angles)
E is mid point of BC and F is mid point of AC
EF parallel to AB, By mid point theorem of triangle.
Therefore, ∠ADF = ∠DFE = 80° ( ∵ EF || AB , Alternate interior angles)
Similarly,
∠DEF = 40°
∠EDF = 60°
The measurements of angles of triangle formed by joining the mid points of the sides of the triangle are 40° , 60° and 80°
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