 # 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

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

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

Classification of Triangles According 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 10

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: