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Warm-Up Judging by appearances, will the lines intersect? 1. 2. Name the plane represented by each surface of the box. 3. the bottom 4. the top 5. the front Angles • Objective 2.02 Apply properties, definitions and theorems of angles and lines to solve problems 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. Name the angle below in four ways. The name can be the number between the sides of the angle: 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. 3 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. 4 Types of Angles Con’t 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. Straight Angle 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: 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. 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 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. 3 is not marked as a right angle, so you cannot conclude that it is a right angle 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 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° 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) On Your Own m LNV = _________ m LNB = 31 m LJC = _________ m GJC = 77 Homework: What Do You Call It When 50 People Stand on a Wooden Deck?