Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.
Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem.
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Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem Chapter 3: rallel and Perpendicular L
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Transcript of Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem.
Section 3-4:Parallel Lines and the Triangle Angle-Sum
Theorem
Chapter 3:Parallel and Perpendicular Lines
Objectives
To classify triangles and find the measures of their angles.To use exterior angles of triangles.
Vocabulary
Acute TriangleRight TriangleObtuse TriangleEquiangular TriangleEquilateral TriangleIsosceles TriangleScalene TriangleExterior Angle of a PolygonRemote Interior Angles
Theorem 3-12:“Triangle Angle-Sum Theorem”
The sum of the measures of the angles of a triangle is 180º
Applying the Triangle Angle-Sum Theorem
Find the values of the variables.
Classification of TrianglesAccording to Angles
Acute- All three angles are acute.Right- One angle is a right angle.Obtuse- One angle is an obtuse angle.Equiangular- All three angles are equal
Classification of TrianglesAccording to Sides
Equilateral- All three sides are congruent.Isosceles- At least two sides are congruent.Scalene- No sides are congruent.
Classifying Triangles
Classify the triangle according to both its sides and angles.
6
11
1075
70 60
Exterior Angle of a Polygon
An exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side.
Exterior Angle
Remote Interior Angles
For each exterior angle of a triangle, the two non-adjacent interior angles are its remote interior angles.
Exterior Angle
Remote Interior Angles
Theorem 3-13:“Triangle Exterior Angle Theorem”
The measure of each exterior angle of a triangle equals the sum of its two remote interior angles.
Using the Triangle Exterior Angle Theorem
Find each angle measure:
