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Chapter 1

Chapter 1 . 1-3 Measuring and constructing angles. Warm up . Instructions: Answer the following questions P1. M is between N and O . MO = 15, and MN = 7.6. Find NO . P2. S is the midpoint of TV , TS = 4x – 7, and SV = 5 x – 15. Find TS , SV , and TV .

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Chapter 1

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  1. Chapter 1 1-3 Measuring and constructing angles

  2. Warm up • Instructions: Answer the following questions • P1. M is between N and O. MO = 15, and MN = 7.6. Find NO. • P2. S is the midpoint of TV, TS = 4x – 7, and • SV = 5x – 15. Find TS, SV, and TV. • P3. LH bisects GK at M. GM =2x + 6, and • GK = 24.Find x.

  3. Warm up Answers • Instructions: Answer the following questions • P1. M is between N and O. MO = 15, and MN = 7.6. Find NO. • Answer: 22.6 • P2. S is the midpoint of TV, TS = 4x – 7, and • SV = 5x – 15. Find TS, SV, and TV. Answer: 25,25,50 • P3. LH bisects GK at M. GM =2x + 6, and • GK = 24.Find x. • Answer: x=3

  4. Objectives • The students will be able to: • * Name and classify angles. • *Measure and construct angles and angle • bisectors.

  5. 1-3 Measuring and constructing Angles • What is an angle? • Answer: is a figure formed by two rays, or sides, with a common endpoint called the vertex(plural: vertices). How can we name an angle? Answer: You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

  6. 1-3 measuring and constructing angles • 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. • Examples of naming angles can be: Angle Name R, SRT, TRS, or 1

  7. 1-3 measuring and constructing angles • Example 1: • A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. • Answer:BAC, CAD, BAD

  8. 1-3 measuring and constructing angles • Example 2: Name the following angles in three different ways

  9. 1-3 measuring and constructing angles • The measureof an angle is usually given in degrees. Since there are 360° in a circle, one degreeis 1/360 of a circle. When you use a protractor to measure angles, you are applying the following postulate:

  10. 1-3 Measuring and constructing angles • You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor. • If OC corresponds with c and OD corresponds with d, • mDOC= |d– c| or |c– d|.

  11. 1-3 measuring and constructing angles • Example 3: • Example problem types • 1.  Measure the following angles.  If necessary, continue the sides of the angle..

  12. 1-3 measuring AND CONSTRUCTING ANGLES • Example 3: • Measuring angles online • Measuring Angles with a Protractor - Welcome to Math Playground • www.mathplayground.com/measuringangles.html

  13. 1-3 measuring and constructing angles

  14. 1-3 measuring and constructing angles • Example 5: • Find the measure of each angle. Then classify each as acute, right, or obtuse. • A. WXV • mWXV =180-150= 30° • WXV is acute. B. ZXW mZXW= |130° - 30°| = 100 ZXW = is obtuse

  15. 1-3 measuring and constructing angles • What are congruent angles?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.

  16. 1-3 measuring and constructing angles

  17. 1-3 measuring and constructing angles • Example 6: • Problem 1 from the angle addition postulate worksheet 1) Find if • and • Solution: • angle addition postulate • substitute values and simplify

  18. 1-3 measuring and constructing angles • Example 7: • Problem 8from the angle addition postulate worksheet • Find if and • Solution: • angle addition 176=x+130 substitute values and solve • -130 -130 • 46=x

  19. 1-3 measuring and constructing angles • Example 8 Problem 11 from the angle addition postulate worksheet ) and Find x. Solution angle addition postulate substitute vales and simplify simplify solve for x X=9

  20. 1-3 measuring and constructing angles • What is an angle bisector ? • Solution: • An angle bisector is a ray that divides an angle into two congruent angles. • JK bisects LJM; thus LJKKJM.

  21. 1-3 measuring and constructing angles • Example 9 • Problem 13 from the angle bisector worksheet Find x if and • Solution • angle bisector • simplify and solve for x • X=7

  22. Student guided practice • Naming Angles 5-8 • Angles and their measures 3-6 • Angle addition Postulate worksheet 2-4 14-16 • Angle bisector worksheet 14-16

  23. Homework • Angle Bisector worksheet 1,2 • Angle Addition Postulate worksheet 7-9 • Page 24 from book do 4-6

  24. Closure • Today we learned about naming and measuring the angles. We also learned about the angle addition postulate and the angle bisector. Tomorrow we are going to continue with lesson 1-4.

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