Applying Parallel Lines to Polygons

Section 3-4

Angles of a Triangle

Review of Major Points

Triangle definition: the figure formed by three segments joining three noncollinear points.

A

B

C

Triangle ABC (DABC)

Vertices of DABC: points A, B, C

Sides of DABC:

Angles of DABC: A, B, C

, ,AB BC CA

Classifying Triangles

By the number of congruent sides it has.Scalene triangle: No sides Isosceles triangle: At least two sides Equilateral triangle: All sides

By their angles.Acute triangle:

Three acute anglesObtuse triangle:

One obtuse angleRight triangle:

One right angleEquiangular triangle:

All angles

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

Corollaries from the theorem: A statement that can be proved easily by applying a theorem is called a corollary.

• 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 measure 60.

• 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.

A

B

C1

2

3

4

D

Theorem 3-12 – Exterior Angle TheoremThe measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

When one side of a triangle is extended, an exterior angle is formed.

The exterior angle is a supplement of the adjacent interior angle.

The other two interior angles in the triangle are referred to as the remote interior angles.

Exterior Angle

Remote Interior Angles

Therefore, by the Exterior Angle Theorem:

m4 = m1 + m3