Triangle Sum Property

Method 1:

Using a ruler and pencil draw an acute triangle and name the vertices as A, B and C.  Cut the triangle ABC. Now cut the 3 corners of the triangle without altering the angle measures of A, B and C. Arrange the 3 corners so that the vertices coincide and the arms (sides) of the angle touch each other. What do you observe? Use the angle addition postulate, predict the sum of the 3 angles of the triangle.

Repeat the above procedure with a right scalene triangle and with an obtuse scalene triangle. Do all of these support the prediction on the sum of the 3 angles of a triangle?

Method 2: Using a ruler and pencil draw an acute scalene triangle, a right scalene triangle and an obtuse scalene triangle and name the vertices as A, B and C.  Using a protractor, measure the three angles of the triangle and tabulate the measures in each case.

 Triangle type Angle A Angle B Angle C ∟A +∟B + ∟C acute scalene right scalene obtuse scalene

What do you observe?

Method 3: Using the segment tool in the Geometer’s sketchpad, draw an acute scalene triangle, an acute isosceles triangle, a right scalene triangle, c triangle, an obtuse scalene triangle and an obtuse isosceles triangle and name the vertices as A, B and C.  Using the measurement menu, measure the three angles of the triangle and tabulate the measures in each case.

 Triangle type Angle A Angle B Angle C ∟A +∟B + ∟C acute scalene right scalene obtuse scalene

What do you observe?

Verify your prediction/ observation. The link below will open in a new window.