Geometry Section 4.1 Triangle Sum Theorem

A triangle is the figure formed by three line segments joining three noncollinear points. A B C

Goals for today’s class: 1. Classify triangles according to their angles and sides. 2. Know and apply the Triangle Sum Theorem. 3. Know and apply the Exterior Angle Theorem. 4. Identify new vocabulary terms.

Triangles are classified according to their angles and sides. Angle classification: Side classification: equiangular equilateral acute isosceles right scalene obtuse 3 congruent angles 3 acute angles 1 right angle 1 obtuse angle 3 congruent sides 2 congruent sides 0 congruent sides

Examples: Classify each triangle according to its angles and sides.

Theorem 4.1: Triangle Sum Theorem The sum of the measures of the three angles of a triangle is ____. (Proof on p.196 of the text)

Examples: Find the value of x.

The angle of x° in example b) is called an exterior angle of the triangle. An exterior angle of a triangle is formed by extending a side of the triangle. Note that the exterior angle will form a _________with an interior angle of the triangle. linear pair

In example b) we found x to equal 136. Note that ____________. This work leads us to the following theorem.

Theorem Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. For the triangle to the right,

Example: Find the value of x.

A corollary is a statement easily proven using a particular theorem.

Example c) on the previous page illustrates the following corollary: Corollary to the Triangle Sum Theorem The acute angles of a right triangle are _____________. complementary