Proving the Interior Angle Sum Theorem
Proving the Interior Angle Sum TheoremAdapted from Walch Education
1.9.1: Proving the Interior Angle Sum Theorem2Triangles Classified by Angle Measure
Acute triangleObtuse triangleRight triangleAll anglesare less than 90.One angleis greater than 90.One anglemeasures 90.
1.9.1: Proving the Interior Angle Sum Theorem3Triangles Classified by Side Lengths
Scalene triangleIsosceles triangleEquilateral triangleNo congruent sides
At least two congruent sides
Three congruent sides
1.9.1: Proving the Interior Angle Sum Theorem4Triangle Sum Theorem
TheoremTriangle Sum Theorem The sum of the angle measures of a triangle is 180.
mA + mB + mC = 180
The Triangle Sum Theorem can be proven using the Parallel Postulate.The Parallel Postulate states that if a line can be created through a point not on a given line, then that line will be parallel to the given line.This postulate allows us to create a line parallel to one side of a triangle to prove angle relationships.
1.9.1: Proving the Interior Angle Sum Theorem5Triangle Sum Theorem1.9.1: Proving the Interior Angle Sum Theorem6Parallel Postulate
PostulateParallel Postulate Given a line and a point not on it, there exists one and only one straight line that passes through that point and never intersects the first line.
Notice that C and D are supplementary; that is, together they create a line and sum to 180.
1.9.1: Proving the Interior Angle Sum Theorem7Interior Angles, Exterior Angles, and Remote Interior Angles
Interior angles: A, B, and C Exterior angle: DRemote interior angles of D: A and B
1.9.1: Proving the Interior Angle Sum Theorem8Exterior Angle Theorem
TheoremExterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
mD = mA + mB
1.9.1: Proving the Interior Angle Sum Theorem9Exterior Angle Inequality Theorem
TheoremExterior Angle Inequality Theorem If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles.
mD > mA mD > mB
1.9.1: Proving the Interior Angle Sum Theorem10More Theorems
TheoremIf one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
mA < mB < mC a < b < c
TheoremIf one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.Thanks for Watching!Ms. DambrevilleWhat You Need (Geneside II)FlightCrank, @ www.emusic.com. Download, play, burn MP3s @ www.emusic.com.What You Need, track 040Other399521.78 - www.emusic.com/albums/28415/
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