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Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem

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Objectives To classify triangles and find the measures of their angles. To use exterior angles of triangles.

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Vocabulary Acute Triangle Right Triangle Obtuse Triangle Equiangular Triangle Equilateral Triangle Isosceles Triangle Scalene Triangle Exterior Angle of a Polygon Remote Interior Angles

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Theorem 3-12: “Triangle Angle-Sum Theorem” The sum of the measures of the angles of a triangle is 180º

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Applying the Triangle Angle-Sum Theorem Find the values of the variables.

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Classification of Triangles According 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

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Classification of Triangles According to Sides Equilateral- All three sides are congruent. Isosceles- At least two sides are congruent. Scalene- No sides are congruent.

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Classifying Triangles Classify the triangle according to both its sides and angles. 6 11 10

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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

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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

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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.

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Using the Triangle Exterior Angle Theorem Find each angle measure:

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