How to Prove the Angle Sum Property of a Triangle
Draw a line parallel to side BC of the triangle that passes through the vertex A.. Write the equation angle PAB + angle BAC + angle CAQ = 180 degrees.. State that angle PAB = angle ABC and angle CAQ = angle ACB.
Steps
1
Draw a line parallel to side BC of the triangle that passes through the vertex A
Draw a line parallel to side BC of the triangle that passes through the vertex A.
2
Write the equation angle PAB + angle BAC + angle CAQ = 180 degrees.
Write the equation angle PAB + angle BAC + angle CAQ = 180 degrees.
3
State that angle PAB = angle ABC and angle CAQ = angle ACB.
State that angle PAB = angle ABC and angle CAQ = angle ACB.
4
Substitute angle PAB and angle CAQ in Equation 1 for angle ABC and angle ACB (as
Substitute angle PAB and angle CAQ in Equation 1 for angle ABC and angle ACB (as found in Equation 2 and Equation 3) respectively.
5
Define the angle sum property.
Define the angle sum property.
6
Study examples.
Study examples.
7
Use the theorem to solve for an unknown angle.
Use the theorem to solve for an unknown angle.
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