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Lesson 1-4

Lesson 1-4. Angle Measure. Transparency 1-4. D. E. A. C. -4. -2. 0. 2. 4. 6. 8. 10. D. E. F. G. H. 5-Minute Check on Lesson 1-3. Use the number line to find each measure. AC DE Find the midpoint of EG Find the distance between P (-2,5) and Q (4,-3) .

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Lesson 1-4

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  1. Lesson 1-4 Angle Measure

  2. Transparency 1-4 D E A C -4 -2 0 2 4 6 8 10 D E F G H 5-Minute Check on Lesson 1-3 • Use the number line to find each measure. • AC • DE • Find the midpoint of EG • Find the distance between P (-2,5) and Q (4,-3). • Find the coordinates of R, if M (-4,5) is the midpoint of RS and S has coordinates of (0,-10)? • What is the perimeter of ∆DEF if its vertices are D(-2,-6), E(-2,6), and F(3,-6)? Standardized Test Practice: A 12 units B 13 units C 17 units D 30 units Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 1-4 D E A C -4 -2 0 2 4 6 8 10 D E F G H 5-Minute Check on Lesson 1-3 • Use the number line to find each measure. • AC • DE • Find the midpoint of EG • Find the distance between P (-2,5) and Q (4,-3). • Find the coordinates of R, if M (-4,5) is the midpoint of RS and S has coordinates of (0,-10)? • What is the perimeter of ∆DEF if its vertices are D(-2,-6), E(-2,6), and F(3,-6)? 4 9 F 10 (-8, 20) Standardized Test Practice: A 12 units B 13 units C 17 units D 30 units Click the mouse button or press the Space Bar to display the answers.

  4. Objectives • Measure and classify angles • Identify and use congruent angles and the bisector of an angle

  5. Vocabulary • Degree – one three hundred and sixtieth of a circle • Ray – part of a line with one end point • Opposite rays – are collinear rays with the same end point (& form a 180 degree angle) Angle is formed by 2 noncollinear rays with a common endpoint (vertex) • Sides – composed of rays • Vertex – is the common endpoint • Interior – area between the two rays that form the angle • Exterior – area not between the two rays that form the angle

  6. Vocabulary (cont) Special types of angles: • Right angle – measure equals 90 degrees • Acute angle – measure is less than 90 degrees • Obtuse angle – measure is greater than 90 degrees (but less than 180) • Angle Bisector – a ray that divides an angle into two congruent angles

  7. Angles 360º A Circle Exterior of angle Ray VA Interior of angle AVB Vertex (hinge point) B Ray VB Angles measured in degrees A degree is 1/360th around a circle Acute Right Obtuse A A A mA < 90º mA = 90º 90º < mA < 180º

  8. Answer: and or are the sides of 5. Example 4-1a Name all angles that have B as a vertex. Answer:5, 6, 7, and ABG Name the sides of 5. Write another name for 6. Answer:EBD, FBD, DBF, and DBE are other names for 6.

  9. a. Name all angles that have X as a vertex. b. Name the sides of 3. Answer: c. Write another name for 3. Example 4-1d Answer:1, 2, 3, and RXB or RXN Answer:AXB, AXN, NXA, BXA

  10. Answer: is a right angle. Example 4-2a Measure TYV and classify it as right, acute, or obtuse. TYV is marked with a right angle symbol, so measuring is not necessary.

  11. Use a protractor to find that . Answer: > is an obtuse angle. Example 4-2b Measure WYT and classify it as right, acute, or obtuse.

  12. With lines ZE and CX and ray ZD, measure each angle named and classify it as right, acute, or obtuse. E D X C Z Example 4-2d a.CZD b.CZE c.DZX Answer: 150, obtuse Answer: 90, right Answer: 30, acute

  13. Both WVX and ZVY measure 90° Answer: Example 4-3d SIGNS A railroad crossing sign forms congruent angles. In the figure, WVX =ZVY. If mWVX = 7a + 13and mZVY = 10a – 20, find the actual measurements of WVXandZVY. WVX  ZVY 7a + 13 = 10a – 20 7a + 33 = 10a 33 = 3a 11 = a WVX = 7(11) + 13 = 90°

  14. Summary & Homework • Summary: • Angles are classified as acute, right, or obtuse according to their measure • An angle bisector is a ray that divides an angle into two congruent angles (halves) • Homework: pg 33-35; 9, 11, 13, 14, 20, 24-26, 50

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