Objectives State the triangle angle sum theorem and solve for an unknown angle in a triangle Classify triangles based on measures of angles as well sides State the triangle exterior angle theorem and solve for an unknown exterior angle of a triangle ID: 278556
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Slide1
1
Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem
Objectives
State the triangle angle sum theorem and solve for an unknown angle in a triangle
Classify triangles based on measures of angles as well sides
State the triangle exterior angle theorem and solve for an unknown exterior angle of a triangleSlide2
2
Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180
°.
m
∠A + m∠B + m∠C = 180
A
B
C
Ex: If m
∠A = 30 and m∠B = 70;
what is m∠C ?
m
∠
A + m
∠
B + m
∠
C = 180
30 + 70 + m∠C = 180
100 + m∠C = 180
m∠C = 180 – 100 = 80
Slide3
3
Classifying TrianglesSlide4
4
Exterior and remote interior angles
An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side
For each exterior angle of a triangle, the two nonadjacent interior angles are called the remote interior anglesSlide5
5
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
m
∠1 = m∠2 + m∠3
Ex: If m∠2 = 45 and m∠3 = 55, what is m∠1?
m∠1 = 45 + 55 = 100