1. Triangles and Angles

2. Definition of a triangle
A triangle is three segments joined at three noncollinear end points.

3. Types of Triangles by Sides
3 Sides congruent → Equilateral

4. Types of Triangles by Sides
2 Sides congruent → Isosceles

5. Types of Triangles by Sides
No Sides congruent → Scalene

6. Types of Triangles by Sides
3 Sides congruent → Equilateral
2 Sides congruent → Isosceles
No Sides congruent → Scalene

7. Types of Triangle by Angles
All Angles less than 90 degrees → Acute

8. Types of Triangle by Angles
One Angle greater than 90 degrees, but less than 180° → Obtuse

9. Types of Triangle by Angles
One Angle equal to 90 degrees → Right

10. How to classify a triangle
Choose one from each category Sides Angles____ Scalene Acute Isosceles Right Equilateral Obtuse

11. Equiangluar All the angles are Equal
Equilateral Triangles are ALWAYS Equilateral

12. Parts of the Right Triangle
Legs- sides of a right triangle
Hypotenuse- the side across from the right angle.

13. Interior Angles vs. Exterior AnglesM a
N b c P
Interior angles: <a, <b, <c
Exterior angles: <M, <N, <P

14. Corollary-a theorem with a proof that follows as a direct result of another theorem.
Corollary 1.) The acute angles of a right triangle are complementary.
Corollary 2.) There can be at most one right or one obtuse angle in a triangle.

15. m<a + m<b + m<c = 180°
Triangle Sum Theorem
The sum of the three interior angles of a triangle is 180º a
b c
m<a + m<b + m<c = 180°

16. Triangle Sum Theorem
Solve for x

17. Example 2
Find the measure of each angle.
2x + 10 x
x + 2

18. Exterior Angle Theorem
The measure of an exterior angle equals the measure of the two nonadjecent interior angles.

19. Example 3 Given that ∠ A is 50º and ∠B is 34º, what is the measure of
∠BCD?
What is the measure of ∠ACB? D A B C

20. Example 4:Solve for x

21. Corollary for the fact that interior angles add to 180º
The acute angles of a Right triangle are complementary.

22. Example 5
A. Given the following triangle, what is the length of the hypotenuse?
B. What are the length of the legs?
C. If one of the acute angle measures is 32°, what is the other acute angle’s measurement? 13 12 5

23. Example 6
Find the missing measures
80°
53°

24. Example 7 Given: ∆ABC with mC = 90° Prove: mA + mB = 90° Statement
Reason
1. mC = 90°
2. mA + mB + mC = 180°
3. mA + mB + 90° = 180°
4. mA + mB = 90°