This document provides definitions and properties related to triangles: - It defines different types of triangles based on sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). - It identifies key parts of triangles like vertices, adjacent/opposite sides, hypotenuse, legs, and base. - It describes interior and exterior angles and states the Triangle Sum Theorem that the interior angles sum to 180 degrees. - The Exterior Angle Theorem and corollary relating right triangles are also presented.

1. 4.1 Triangles and Angles Objectives: - Classify triangles by their sides and angles - Find angle measures

2. Names of Triangles - by sides Equilateral 3 congruent sides Isosceles At least 2 congruent sides Scalene No congruent sides

3. Names of Triangles - by angles Acute 3 acute angles Equilateral 3 congruent angles Right 1 right angle Obtuse 1 obtuse angle

4. When you classify a triangle... Be as specific as possible. acute scalene A B C 65˚ 57˚ 58˚

5. When you classify a triangle... What is this one? obtuse isosceles 120˚

6. Terms Each of the 3 points joining the sides of a triangle is a vertex 2 sides sharing a common vertex are adjacent sides A B C

7. Right Triangles In a right triangle, the side opposite the right angle is called the hypotenuse The sides opposite the two acute angles are called legs A B C 50° q r s

8. Isosceles Triangles If an isosceles triangle has 3 congruent sides, it is equilateral. If an isosceles triangle has 2 congruent sides, the sides are the legs of the triangle, and the 3rd side is the base of the triangle.

9. Identifying parts What kind of triangle is this? isosceles right Which side is the hypotenuse? Which side is the base? Which sides are the legs? 5” 5” 7”

10. Interior & Exterior Angles Interior angles are inside the triangle. Exterior angles are adjacent to the interior angles. Each vertex has a pair of congruent exterior angles.

11. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180˚.

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.

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

14. Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary.

15. Classwork Do p. 198 1-15 together