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1.4: Angle Measure

1.4: Angle Measure. SOL: G4 Objectives: Measure and classify angles. Identify special angle pairs. Use the special angle pairs to find angle measures. B. Noncollinear rays. A. A. C. Common Endpoint. Angle. formed by two noncollinear rays that have a common endpoint. Side AB.

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1.4: Angle Measure

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  1. 1.4: Angle Measure • SOL: G4 • Objectives: • Measure and classify angles. • Identify special angle pairs. • Use the special angle pairs to find angle measures.

  2. B Noncollinear rays A A C Common Endpoint Angle • formed by two noncollinear rays that have a common endpoint.

  3. Side AB B A A Vertex A C Side AC Sides of an Angle • The rays that make the angle Vertex of an Angle • The common endpoint

  4. B A 4 C Note the vertex is the middle point listed Symbols • When we name an angle, the vertex point is always in the middle • The following are the different ways we can name this angle: A, BAC, CAB, 4

  5. Any point inside the angle Exterior Exterior Interior of an Angle Exterior of an Angle • Any point outside the angle Interior

  6. BG and BE or BF Example 1: Use the diagram to answer a, b, and c. a.) Name all angles that have B as a vertex. b.) Name the sides of 5. c.) Write another name for 6. ∡ABG, ∡ABD, ∡DBE or ∡DBF, ∡EBG or ∡FBG, ∡5, ∡6, ∡7 ∡DBE or ∡DBF

  7. Measuring Angles The protractor has two scales running from 0 to 180 degrees in opposite directions. These are the scales we use to determine the measure of the angle Place the center point of the protractor on the vertex Align the 0 on either side of the scale with one side of the angle. (Paying attention to which direction the angle is opening To measure an angle, you use a protractor.

  8. Example 2: Since QP is aligned with the 0 on the outer scale, use the outer scale to find that QR intersects the scale at 65 degrees. Find the measure of PQR. R 65° Q P

  9. Measures 90 Written as mA = 90 A This symbol means, right angle, perpendicular B Classify Angles by Angle Measure Right Angle Acute Angle • Measures less than 90 • Written as mB < 90

  10. A B C C Classify Angles by Angle Measure Obtuse Angle Straight Angle (Line) • Measures greater than 90 • Measures 180 • Written as mC > 90

  11. Example 3: Measure the angle and classify it. 12°, Acute

  12. Example 4: Measure the angle and classify it. 99°, Acute

  13. Example 5: Measure the angle and classify it. 69°, Acute

  14. Congruent Angles • Angles that have the same measure • Symbols: NMPQMR

  15. Postulate 1.8: Angle Addition Postulate • If point B is in the interior of ∠AOC , then m∠AOB + m∠BOC = m∠AOC

  16. Example 6: M If m∠EFG = 23°, what is the m∠EFH? D 12° Apply the angle addition postulate. A m∡EFG - m∡GFH = m∡EFH 23° K 23° - 11° = 12° C 68° L 46° H J B E If m∠KJL = 117°, what is the m∠KJM? What is the m∡ABC? 11° G 69° 49° m∡ABD + m∡CBD = m∡ABC m∡KJL - m∡LJM = m∡KJM 23° + 46° = 69° F 117° - 68° = 49°

  17. Example 7: If m∠RQT = 155°, what are the m∠RQS and m∠SQT? m∡RQS + m∡TQS = m∡RQT Check: 72° + 83° = 155° (4x – 20) + (3x + 14) = 155° 7x – 6= 155° + 6 + 6 7x = 161° 7x = 161° 7 7 x = 23° m∡RQS = 4x – 20 = 4(23) – 20 = 72° m∡TQS = 3x + 14 = 3(23) + 14 = 83°

  18. Example 8: ∠DEF is a straight angle. What are the m∠DEC and m∠CEF? m∡DEC + m∡FEC = m∡DEF (11x – 12) + (2x + 10) = 180° 13x – 2 = 180° + 2 + 2 13x = 182° Check: 142° + 38° = 180° 13x = 182° 13 13 x = 14° m∡DEC = 11x – 12 = 11(14) – 12 = 142° m∡FEC = 2x + 10 = 2(14) + 10 = 38°

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