2. Goal, to classify triangles by their sides and by their angles.

3. Equilateral triangle, 3 congruent sides. Isosceles triangle, at least 2 congruent sides Scalene triangle, no congruent sides. Classification of triangles by SIDES

4. Equiangular Triangle; 3 congruent angles Acute Triangle; 3 acute angles Classification of triangles by ANGLES Right triangle; 1 right angle Obtuse triangle; 1 obtuse angle

7. The angles that are adjacent to the interior angles are the exterior angles. 1 3 2 The three angles of a triangle are called the INTERIOR ANGLES interior angles When the sides of a triangle are extended, other angles are formed. A B C

8. The sum of the measures of the angles of a triangle is 180°. m  + m  + m  = 180° A C B A B C

9. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. m  A + m  B = 90°. A B C

10. Exterior Angle A B 1 C Exterior angle 120 60 The exterior angle and the adjacent interior angle are supplementary.

11. Exterior Angle Theorem A B C 130 5030 100 30 130 +=

12. Exterior Angle Theorem A B C 145 3550 95 50 145 +=

13. 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 (remote interior angles). m  A + m  B = m  1 A B 1 C

14. 55 46 ? Triangle Sum Theorem (1) 79

15. x+5 3x 15 (2) (x+5)+3x+15 = 180 4x+20 = 180 4x = 160 x = 40

16. 161 73 ? (3) 19 92

17. 116 63 x? (4) 25 35 y? 91 119