1. Introduction to Angles and Triangles

2. Degrees: Measuring Angles
We measure the size of an angle using degrees.
Example: Here are some examples of angles and
their degree measurements.

3. Acute Angles
An acute angle is an angle measuring between 0 and 90 degrees.
Example:
                                                               

4. Obtuse Angles
An obtuse angle is an angle measuring between 90 and 180 degrees.
Example:
                                                                 

5. Examples: Straight Angle
A right angle is an angle measuring 180 degrees.
Examples:
                                      

6. Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary.
                                                                      

7. These two angles can be "pasted" together to form a straight line!
                                                

8. Example: Complementary Angles
Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary.
                                                      
                        

9. These two angles can be "pasted" together to form a right angle!
                        

10. Review State whether the following are acute, right, or obtuse. acute3. 5. 1.
right
obtuse ? 4. 2.
acute ?
obtuse

11. Complementary and Supplementary
Find the missing angle.
1. Two angles are complementary. One measures 65 degrees.
2. Two angles are supplementary. One measures 140 degrees.
Answer : 25
Answer : 40

12. Complementary and Supplementary
Find the missing angle. You do not have a protractor.
Use the clues in the pictures. 2. 1. x x 55
165
X=35
X=15

13. 1. x
x = 90 y z
y =
z =
x = 2. x
110 y z
y =
z =

14. Vertical Angles are angles on each side of intersecting lines
                    1. 90 x y z 90
90 and y are vertical angles
x and z are vertical angles
The vertical angles in this case are
equal, will this always be true?
110 70
110 x y z
110 and y are vertical angles 2.
x and z are vertical angles
Vertical angles are always equal

15. Vertical Angles Find the missing angle. Use the clues in the pictures.x
X=58 58

16. Can you find the missing angles?20 90 D 70 G C 70 90 20 J H

17. Can you find these missing anglesB C 68 A 52 G 60 D 60 52 68 F E

18. Can be classified by the angle measures
Triangles
Can be classified by the angle measures

19. Has three acute angles (less than 90 degrees)
Acute Triangle
Has three acute angles (less than 90 degrees)

20. Triangle with one obtuse angle (greater than 90 degrees)
Obtuse Triangle
Triangle with one obtuse angle (greater than 90 degrees)

21. Has one right angle (90 degree)
Right Triangle
Has one right angle (90 degree)

22. Can be classified by the number of congruent sides
Triangles
Can be classified by the number of congruent sides

23. Has no congruent sides (all angles, and sides are different)
Scalene Triangle
Has no congruent sides (all angles, and sides are different)

24. Has at least two congruent sides
Isosceles Triangle
Has at least two congruent sides

25. All three sides are congruent
Equilateral Triangle
All three sides are congruent

26. Which can only happen in a equalateral triangle
Equiangular Triangle
Triangle with 3 equal angles
Which can only happen in a equalateral triangle

27. Triangles Cut any shape triangle out of a sheet of paper .
Tear off the corners. Piece them together by having the corners touch.
The corners form what type of angle?

28. The sum of the angles of a triangle is 180 degrees
Triangles
The sum of the angles of a triangle is 180 degrees

29. If all the angles must add to 180 and be the same…..
Equiangular Triangle
Triangle with 3 equal angles
If all the angles must add to 180 and be the same…..
Then,
x+x+x = 180
3x = 180
X = 60

30. If you know 2 angles, then you can always figure out the 3rd
Triangles
If you know 2 angles, then you can always figure out the 3rd

31. Triangle Inequalities

32. Triangle Inequality Theorem:
The sum of two smaller sides of a triangle must be greater than the length of the largest side.
a + b > c
a + c > b
b + c > a
Example:
Determine if it is possible to draw a triangle with side measures 12, 11, and 17.
> 17  Yes
> 12  Yes
> 11  Yes
Therefore a triangle can be drawn.

33. Angle Side Relationship
The longest side is across from the largest angle.
The shortest side is across from the smallest angle. 54 37 89 B C A
BC = 3.2 cm
AB = 4.3 cm
AC = 5.3 cm

34. Triangle Inequality – examples…
For the triangle, list the angles in order from least to greatest measure. C A B
4 cm
6 cm
5 cm

35. Triangles

36. Congruent Triangles

37. The Idea of a Congruence
Two geometric figures with exactly the same size and shape. A C B D E F

38. Congruent Triangles
Have congruent corresponding parts, sides and angles May be flipped and/or rotated BE CAREFUL WHEN YOU NAME THE SHAPE

39. Congruent Triangles are named such that the corresponding angles are in the same order

40. Write the congruence statementB F E D A C

41. Name the congruent triangles
List the congruent sides and angles
Angles Sides