1. 3-4 Angles of a Triangle

2. A Triangle is a figure formed by three segments joining three noncollinear points. 1) Classifying triangles by their sides. a) Equilateral triangle – 3 congruent sides b) Isosceles triangle - 2 congruent sides c) Scalene triangle - No congruent sides

3. 2) Classifying triangles by their angles. a) Acute triangle - has 3 Acute angles b) Equiangular triangle - has 3 congruent angles - an Equiangular triangle is also Acute. c) Right triangle - has one right angle d) Obtuse triangle - has one obtuse angle

4. Theorems: 1) Theorem 3 - 11 Triangles Sum Theorem The sum of the measures of the interior angles of a triangle is 180° 2) Theorem 3 - 12 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. m<1 = m<B + m<C

5. Problems: 1) Classify the triangle a) b) 2) Find the value of x. Then find the measure of the exterior angle.

6. C) Corollary – to a theorem is a statement that can be proved easily using the theorem. Corollary 4 to the triangle sum theorem. The acute angles of a right triangle are complementary. m<A + m<C = 90°

7. 3) The measure of one acute angle of a right triangle is one-fourth the measure of the other acute angle. Find the measure of each acute angle.

8. Corollary 1 If two angles of one triangle are to two angles of another triangle, then the third angles are. Corollary 2 Each angle of an equiangular triangle has a measure of 60° Corollary 3 In a triangle, there can be at most one right angle or one obtuse angle.

9. Find the values of x and y. 1) 2)