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

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

Goal 2.03 Apply properties, definitions, and theorems of two-

dimensional figures to solve problems and write proofs: a)

Triangles.

Essential Question

How is the Triangle Exterior Angle Theorem applied?

Through a point outside a line, there is exactly one line parallel to the given line.

Through a point outside a line, there is exactly one line perpendicular to the given line.

Exterior angles of a Polygon

exterior angle of a triangle: the angle formed when one side of a triangle is extended.

Remote Interior Angles

remote interior angles: the two angles of a triangle which are not adjacent to a given exterior angle

Corollary

a statement that can be proved easily by applying a theorem

Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle equals the sum of the measures of two remote interior angles.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangle Corollaries (Corollary) If two angles of one triangle are

congruent to two angles of another triangle, then the third angles are congruent.

(Corollary) Each angle of an equiangular triangle has measure 60.

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

(Corollary) The acute angles of a right triangle are complementary.

Examples: p 13524.25.26.27.28.

Independently: p 137: # 44 -47

Group Practice

with a partner: p 136: # 40 p 137: # 42, 43, 48, 49

Independent Practice

Standardized Test Prep: p 138: 64 – 67 all

Summarize: Worksheet: Lesson Quiz 4.2

Homework

Practice 3-3