Applying Parallel Lines to Polygons Lesson 3.4 Pre-AP Geometry

Objectives 1.Classify triangles according to sides and to angles. 2.State and apply the theorem and the corollaries about the sum of the measure of the angles of a triangle. 3.State and apply the theorem about the measure of an exterior angle of a triangle.

Triangle A figure formed by three segments joining three non-collinear points. Each of the three points is called a vertex of the triangle. The segments are the sides of the triangle. A B C

Classifying Triangles There are two ways of classifying triangles by their sides by their angles

Equilateral Triangle All sides are the same length.

Isosceles Triangles At least two sides are the same length

Scalene Triangles No sides are the same length

Acute Triangles Acute triangles have three acute angles

Right Triangles Right triangles have one right angle

Obtuse Triangles Obtuse triangles have one obtuse angle

Equiangular Triangle Equiangular triangles have all congruent angles.

Auxiliary Line A line, not originally a part of a diagram, that is added to more clearly show a relationship. Auxiliary lines are usually shown as dashed lines.

Theorem 3-11 The sum of the measures of the angles of a triangle is 180º.

Definition: Corollary A corollary is a statement which follows readily from a previously proven statement, typically a mathematical theorem.

Corollary 1 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

Corollary 2 Each angle of an equiangular triangle has a measure of 60º.

Corollary 3 In a triangle, there can be at most one right angle or obtuse angle.

Corollary 4 The acute angles of a right triangle are complementary.

Definitions Exterior Angle An angle that forms a linear pair with one of the interior angles of the triangle. Remote Interior Angles In a triangle, the two angles that are non- adjacent to the exterior angle of interest.

Theorem 3-12 The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles. A B C