1. Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

2. 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.

3. 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.

4. 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.

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

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

7. 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.

8. Theorem 4.1 Triangle Sum Theorem: The sum of the measures of the interior angles of a triangle is 180 o. 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.

9. Ex.4: Find. Ex.5: Find the measure of in the diagram shown.

10. 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.

11. 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.

12. Ex.7: Find Ex.8: Find the measure of each interior angle of ∆ABC, where

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