1. Angles and their measurements

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. Right Angles A right angle is an angle measuring 90 degrees. Examples:

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

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

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

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

10. Vertical Angles For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Angle BEC and angle AED are also vertical angles. Vertical angles have the same degree measurement.

11. Review State whether the following are acute, right, or obtuse. 1. 2. 3. 4. 5. ? ? acute obtuse right obtuse acute

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

13. Complementary and Supplementary Find the missing angle. You do not have a protractor. Use the clues in the pictures. 1. 2. x 55165 x X=35 X=15

14. Vertical Angles Find the missing angle. You do not have a protractor. Use the clues in the pictures. 58 x X=58

15. Triangles

16. Triangles A triangle is a 3-sided polygon. Every triangle has three sides and three angles. When added together, the three angles equal 180°.

17. Acute Triangles A triangle in which all three angles are less than 90°.

18. Obtuse Triangles An obtuse triangle is a triangle in which one of the angles is greater than 90°.

19. Right Triangles A right triangle is triangle with an angle of 90°.

20. Scalene Triangles A triangle with three unequal sides.

21. Isosceles Triangles An isosceles triangle is a triangle with (at least) two equal sides.

22. Equilateral Triangles An equilateral triangle is a triangle with all three sides of equal length.

23. Equiangular Triangles An equiangular triangle is a triangle which has three equal angles.

24. Congruent Triangles Congruent triangles are triangles whose corresponding angles and sides are congruent. They are exactly the same size and shape.

25. The Hypotenuse The hypotenuse of a right triangle is the triangle's longest side, i.e., the side opposite the right angle.

26. The Pythagorean Theorem For a right triangle with legs a and b and hypotenuse c, a 2 +b 2 =c 2.

27. Quick Quiz (all together!)

28. Question 1 If a triangle has three unequal sides it is a ______ triangle. – A) Scalene – B) Obtuse – C) Isosceles Answer: – A) Scalene

29. Question 2 A triangle which has three equal angles is a ______ triangle. – A) Acute – B) Equilateral – C) Equiangular Answer: – C) Equiangular

30. Question 3 A triangle with (at least) two equal sides is a ______ triangle. – A) Scalene – B) Isosceles – C) Congruent Answer: – B) Isosceles

31. Question 4 Two triangles that are equal are called ______ triangles – A) Acute – B) Obtuse – C) Congruent Answer: – C) Congruent

32. Question 5 A triangle with all three sides of equal length is a ______ triangle. – A) Equilateral – B) Right – C) Equiangular Answer: – A) Equilateral

33. Question 6 A triangle with an angle of 90° is a ______ triangle. – A) Acute – B) Right – C) Congruent Answer: – B) Right

34. Question 7 A triangle in which all three angles are less than 90° is a ______ triangle. – A) Right – B) Acute – C) Scalene Answer: – B) Acute

35. Question 8 A triangle in which one of the angles is greater than 90° is a ______ triangle. – A) Obtuse – B) Isosceles – C) Acute Answer: – A) Obtuse

36. Question 9 What is the Hypotenuse of a right triangle? – A) The smallest angle. – B) The side opposite the right angle. – C) The right angle. Answer: – B) The side opposite the right angle.

37. Question 10 The Pythagorean Theorem states … – A)  r 2 – B) (a+b) 2 /2=c – C) a 2 +b 2 =c 2 Answer: – C) a 2 +b 2 =c 2

38. Question 11 Use the Pythagorean Theorem to solve the following: – a = 5 – b = 12 – c = ? Answer: – c = 13