Download Lesson 3.4

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.
B
A
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 nonadjacent 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.
B
C
A