Warm-Up

1. Warm-Up Judging by appearances, will the lines intersect? 1. 2. Name the plane represented by each surface of the box. the bottom 3. 4. the top the front 5.

2. Angles • Objective 2.02 Apply properties, definitions and theorems of angles and lines to solve problems

3. We can specify an angle by using a point on each ray and the vertex. The angle below may be specified as angle ABC or as angle CBA; you may also see this written as  <ABC or as  <CBA. Note how the vertex point is always given in the middle.

4. Name the angle below in four ways. The name can be the number between the sides of the angle: 3 The name can be the vertex of the angle: <G. Finally, the name can be a point on one side, the vertex, and a point on the other side of the angle: <AGC, <CGA.

5. 4 Types of Angles Acute Angles An acute angle is an angle measuring between 0 and 90 degrees. Example: The following angles are all acute angles. Obtuse Angles An obtuse angle is an angle measuring between 90 and 180 degrees. Example: The following angles are all obtuse.

6. 4 Types of Angles Con’t Straight Angle Right Angles A right angle is an angle measuring 90 degrees. Two lines or line segments that meet at a right angle are said to be perpendicular. Note that any two right angles are supplementary angles (a right angle is its own angle supplement). Example: The following angles are both right angles. A straight angle is 180 degrees A straight angle changes the direction to point the opposite way. Sometimes people say “ You did a complete 180 on that!" ... meaning you completely changed your mind, idea or direction. All the angles below are straight angles:

7. Name all pairs of angles in the diagram that are: a. vertical Vertical angles are two angles whose sides are opposite rays. Because all the angles shown are formed by two intersecting lines, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. b. supplementary Two angles are supplementary if the sum of their measures is 180. A straight angle has measure 180, and each pair of adjacent angles in the diagram forms a straight angle. So these pairs of angles are supplementary: 1 and 2, 2 and 3 , 3 and 4, and 4 and 1.

8. 3 and 5 are not marked as congruent on the diagram. Although they are opposite each other, they are not vertical angles. So you cannot conclude that 35. Use the diagram below. Which of the following can you conclude: 3 is a right angle, 1 and 5 are adjacent, 3 is congruent to 5? You can conclude that 1 and 5 are adjacent because they share a common side, a common vertex, and no common interior points. 3 is not marked as a right angle, so you cannot conclude that it is a right angle

9. Find the value of x. The angles with labeled measures are vertical angles because their sides are opposite rays. Apply the Vertical Angles Theorem to find x. 4x – 101 =2x + 3

10. Supplementary Angles Two Angles are Supplementary if they add up to 180 degrees These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°. But the angles don't have to be together. These two are supplementary because 60° + 120° = 180°

11. Complementary Angles Two Angles are Complementary if they add up to 90 degrees (a Right Angle). These two angles (40° and 50°) are Complementary Angles, because they add up to 90°. But the angles don't have to be together. These two are complementary because 27° + 63° = 90° • How can you remember which is which? Easy! Think: • "C" of Complementary stands for "Corner"    (a Right Angle), and • "S" of Supplementary stands for "Straight" (180 degrees is a straight line)

12. On Your Own m    LNV = _________m    LNB = 31 m  LJC = _________m  GJC = 77

13. Homework: What Do You Call It When 50 People Stand on a Wooden Deck?