Chapter 4.1 Notes: Apply Triangle Sum Properties

Goal: You will classify triangles and find measures of their angles.

• A triangle is a polygon with three sides.

• A triangle with vertices A, B, and C is called “triangle ABC” or “∆ABC.”

Classifying Triangles by Sides

• A scalene triangle is a triangle with no congruent sides.

• An isosceles triangle is a triangle with at least two congruent sides.

• An equilateral triangle is a triangle with three congruent sides.

Classifying Triangles by Angles

• An acute triangle is a triangle with three acute angles.

• A right triangle is a triangle with one right angle.

• An obtuse triangle is a triangle with one obtuse angle.

• An equiangular triangle is a triangle with three congruent angles.

Ex.1: Classify the triangular shape of the support beams in the diagram by its sides and by measuring its angles.

Ex.2: Classify the triangle shown in the diagram by its sides and angles.

Ex.3: Classify the triangle by its sides and angles.

Angles

• When the sides of a polygon are extended, other angles are formed.

• The original angles are the interior angles.

• The angles that form linear pairs with the interior angles are the exterior angles.

• Theorem 4.1 Triangle Sum Theorem:

The sum of the measures of the interior angles of a triangle is 180o.

• Theorem 4.2 Exterior Angle Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Ex.4: Find .

Ex.5: Find the measure of in the diagram shown.

m JKM

1

• A corollary to a theorem is a statement that can be proved easily using the theorem.

• Corollary to the Triangle Sum Theorem:

The acute angles of a right triangle are complementary.

Ex.6: The tiled staircase shown forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other. Find the measure of each acute angle.

Ex.7: Find

Ex.8: Find the measure of each interior angle of ∆ABC, where

, 2 ,& 3 .o o om A x m B x m C x

.m G

Ex.9: Find the measures of the acute angles of the right triangle in the diagram shown.