1 / 19

Measuring Angles

Measuring Angles. GEOMETRY LESSON 1-6. Use the figure below for Exercises 1 – 3. 1. If XT = 12 and XZ = 21, then TZ = . 2. If XZ = 3 x , XT = x + 3, and TZ = 13, find XZ . 3. Suppose that T is the midpoint of XZ . If XT = 2 x + 11 and XZ = 5 x + 8,

ulysses-mcdaniel
Download Presentation

Measuring Angles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Measuring Angles GEOMETRY LESSON 1-6 Use the figure below for Exercises 1–3. 1. If XT = 12 and XZ = 21, then TZ = . 2. If XZ = 3x, XT = x + 3, and TZ = 13, find XZ. 3. Suppose that T is the midpoint of XZ. If XT = 2x + 11 and XZ = 5x + 8, find the value of x. 9 24 14 Solve each equation. m = 130 7.m – 110 = 20 4. 50 + a = 130 a = 80 x = 135 8.x + 45 = 180 5. 85 – n = 40 n = 45 y = 45 6.z – 20 = 90 9. 180 – y = 135 z = 110 Answers to Lesson Exercises Check Skills You’ll Need 1-5

  2. Measuring Angles GEOMETRY LESSON 1-6 Objectives Find the measure of angles. Identify special angle pairs. 1-6

  3. Measuring Angles GEOMETRY LESSON 1-6 An angleis a figure formed by two rays, or sides, with a common endpoint called the vertex(plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number. 1-6

  4. Measuring Angles GEOMETRY LESSON 1-6 The set of all points between the sides of the angle is the interior of an angle. The exterior of an angleis the set of all points outside the angle. Angle Name R, SRT, TRS, or 1 You cannot name an angle just by its vertex if the point is the vertex of more than one angle. In this case, you must use all three points to name the angle, and the middle point is always the vertex. 1-6

  5. The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degreeis of a circle. When you use a protractor to measure angles, you are applying the following postulate. Measuring Angles GEOMETRY LESSON 1-6 1-6

  6. Measuring Angles GEOMETRY LESSON 1-6 Types of Angles (classified by measure) 1-6

  7. Measuring Angles GEOMETRY LESSON 1-6 Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent. 1-6

  8. Measuring Angles GEOMETRY LESSON 1-6 The Angle Addition Postulate is very similar to the Segment Addition Postulate. 1-6

  9. Measuring Angles GEOMETRY LESSON 1-6 SpecialAngle Pairs 1-6

  10. Measuring Angles GEOMETRY LESSON 1-6 You can make some conclusions directly from diagrams. You canconclude that angles are • adjacent angles • adjacent supplementary angles • vertical angles Unless there are marks that give this information,you cannotassume • angles or segments are congruent • an angle is a right angle • lines are parallel or perpendicular 1-6

  11. 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. Measuring Angles GEOMETRY LESSON 1-6 Name the angle below in four ways. Quick Check 1-6

  12. Use a protractor to measure each angle. m 1 = 110 Because 90 < 110 < 180, 1 is obtuse. m 2 = 80 Because 0 < 80 < 90, 2 is acute. Measuring Angles GEOMETRY LESSON 1-6 Find the measure of each angle. Classify each as acute, right, obtuse, or straight. Quick Check 1-6

  13. m 1 + m 2 = m ABCAngle Addition Postulate. 42 + m 2 = 88Substitute 42 for m 1 and 88 for m ABC. m 2 = 46 Subtract 42 from each side. Measuring Angles GEOMETRY LESSON 1-6 Suppose that m 1 = 42 and m ABC = 88. Find m 2. Use the Angle Addition Postulate to solve. Quick Check 1-6

  14. 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. Measuring Angles GEOMETRY LESSON 1-6 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 1-6

  15. Measuring Angles GEOMETRY LESSON 1-6 (continued) c. complementary Two angles are complementary if the sum of their measures is 90. No pair of angles is complementary. Quick Check 1-6

  16. 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. Measuring Angles GEOMETRY LESSON 1-6 Use the diagram below. Which of the following can you conclude: 3 is a right angle, 1 and 5 are adjacent, 3 5? You can conclude that 1 and 5 are adjacent because they share a common side, a common vertex, and no common interior points. Although 3 appears to be a right angle, it is not marked with a right angle symbol, so you cannot conclude that 3 is a right angle. Quick Check 1-6

  17. Measuring Angles GEOMETRY LESSON 1-6 Use the figure below for Exercises 1–2. 1. Name 2 two different ways. DAB, BAD 2. Measure and classify 1, 2, and BAC. 90°, right; 30°, acute; 120°, obtuse Use the figure below for Exercises 3–4. Sample: 1 and 3, 2 and 4 3. Name a pair of supplementary angles. 4. Can you conclude that there are vertical angles in the diagram? Explain. No; no angle pairs are formed by opposite rays. 1-6

More Related