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

2. Classification By Sides
Classification By Angles

3. Classifying Triangles
In classifying triangles, be as specific as possible.
Obtuse,
Isosceles
Acute,
Scalene

4. Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o. 3 2 1
m<1 + m<2 + m<3 = 180°

5. 60º 90º 30º 60º 180º 30º 90º Property of triangles
The sum of all the angles equals 180º degrees.
60º
90º
30º +
60º
180º
30º
90º

6. 40º 90º 40º 50º 180º 50º 90º Property of triangles
The sum of all the angles equals 180º degrees.
40º
90º
40º
50º +
180º
50º
90º

7. 60º 60º 60º 180º Property of triangles 60º 60º 60º
The sum of all the angles equals 180º degrees.
60º
60º
60º
60º +
180º
60º
60º

8. What is the missing angle?
70º
70º ? ? +
180º
70º
70º
180 – 140 = 40˚

9. What is the missing angle?
90º ?
30º ? +
30º
90º
180º
180 – 120 = 60˚

10. What is the missing angle?
60º
60º ? +
60º
60º
180º
= 6060˚

11. What is the missing angle?
30º
78º ? +
78º
30º
180º
180 – 108 = 72˚

12. Find all the angle measures
45x
10x
35x
180 = 35x + 45x + 10x
180 = 90x
2 = x
90°, 70°, 20°

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

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

15. 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.

16. 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.

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

18. 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.

19. Ex. 6: The tiled staircase shown forms a right triangle
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.

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

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