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Learning Objective: Identify and describe geometric figures Identify angles and angle pairs

Geometry Presentation #1 Building Blocks of Geometry & Classifying Angles April 22, 2013 Math Block 4. Learning Objective: Identify and describe geometric figures Identify angles and angle pairs. Warm Up What geometry term might you associate with each object?

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Learning Objective: Identify and describe geometric figures Identify angles and angle pairs

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  1. Geometry Presentation #1Building Blocks of Geometry & Classifying AnglesApril 22, 2013Math Block 4 Learning Objective: Identify and describe geometric figures Identify angles and angle pairs

  2. Warm Up What geometry term might you associate with each object? 1. one edge of a cardboard box 2. the floor 3. the tip of a pen line segment or line plane or rectangle point

  3. Vocabulary point line plane ray line segment congruent

  4. XY, or YX, or l X Y Use two points on the line or a lowercase letter to name a line. Helpful Hint A number line is an example of a line. A point is an exact location. It is usually represented as a dot, but it has no size at all. point A Use a capital letter to name a point. • A l A lineis a straight path that extends without end in opposite directions.

  5. Q S R Helpful Hint A coordinate plane is an example of a plane. A plane is a Flat surface that Has no thickness and extends forever. plane QRS Use three points in any order, not on the same line, to name a plane.

  6. Additional Example 1: Identifying Points, Lines, and Planes Identify the figures in the diagram. D E F A. three points D, E, and F Choose any two points on a line to name the line. B. two lines DE, DF Choose any three points, not on the same line, in any order. C. a plane plane DEF

  7. Check It Out: Example 1 Identify the figures in the diagram. G H I F A. four points H, G, I, and F Choose any two points on a line to name the line. B. two lines IH, HF Choose any three points, not on the same line, in any order. C. a plane plane IGF

  8. GH Name the endpoint first when naming a ray. G H LM, or ML Use the endpoints to name a line segment. L M A ray is a part of a line. It has one endpoint and extends forever one direction. A line segmentis part of a line. or a ray that extends from one endpoint to another.

  9. Additional Example 2: Identifying Line Segments and Rays Identify the figures in the diagram. M N O A. three rays Name the endpoint of a ray first. MN, NM, MO B. two line segments Use the endpoints in any order to name a segment. MN, MO

  10. Check It Out: Example 2 Identify the figures in the diagram. D C A. three rays Name the endpoint of a ray first. B A BC, CA, BD B. three line segments Use the endpoints in any order to name a segment. BA, CA, BD

  11. Figures are congruent if they have the same shape and size. Line segments are congruent if they have the same length. You can use tick marks to indicate congruent line segments. In the triangle below, line segments AB and BC are congruent.

  12. AB CD ACBD BF DF EC AE Reading Math The symbol means “is congruent to.” Additional Example 3: Identifying Congruent Line Segments Identify the line segments that are congruent in the figure. One tick mark Two tick marks Three tick marks

  13. A AB AC BCDE B C BD CE E D Check It Out: Example 3 Identify the line segments that are congruent in the figure. One tick mark Two tick marks Three tick marks

  14. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  15. AD, BE, CF Possible answer: GA, GB, GC Possible answer: AG, AD, DG, BG AG GD, GB GE Lesson Quiz Identify the figures in the diagram. 1. lines 2. plane Possible answer: plane ABG 3. three rays 4. four line segments 5. Identify the line segments that are congruent in the figure.

  16. Lesson Quiz for Student Response Systems 1. Identify the lines in the diagram. A. B.AB, AE C. D.

  17. Lesson Quiz for Student Response Systems 2. Identify a plane in the diagram. A. plane AFD B. plane EFC C. plane ABC D. plane BGF

  18. Lesson Quiz for Student Response Systems 3. Identify three rays in the diagram. A. B. C. D.

  19. Lesson Quiz for Student Response Systems 4. Identify the line segments that are congruent in the figure. A. B. C. D.

  20. Vocabulary angle vertex right angle acute angle obtuse angle straight angle complementary angles supplementary angles

  21. A Vertex 1 B C An angleis formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex. Angles are measured in degrees (°).

  22. An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle. An acute angle is an angle that measures less than 90°. Anobtuse angle is an angle that measures more than 90° but less than 180°. A straightangle is an angle that measures exactly 180°.

  23. Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. acute angle obtuse angle

  24. Reading Math You can name this angle ABC, CBA, B, or 1. A • 1 B • • C

  25. Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. B. A. straight angle acute angle

  26. If the sum of the measures of two angles is 90°, then the angles are complementary angles. If the sum of the measures of two angles is 180°, then the angles are supplementary angles.

  27. To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mOMP = 60°. P Q O N R M Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ Since 60° + 30° = 90°, PMQ andOMP are complementary.

  28. Reading Math If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle is acute, its measure is less than 90°.

  29. P Q Reading Math O Read mNMO as “the measure of angle NMO.” N R M Additional Example 2B: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. NMO and OMR mNMO = 15° and mOMR = 165° Since 15° + 165° = 180°, NMO andOMR are supplementary.

  30. To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mQMR = 75°. P Q O N R M 8-2 Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR Since 30° + 75° = 105°, PMQ andQMR are neither complementary nor supplementary.

  31. D E C F B A Check It Out: Example 2A Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC andCAF are supplementary.

  32. To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° -35° = 55°. mEAF = 35°. D E C F B A Check It Out: Example 2B Use the diagram to tell whether the angles are complementary, supplementary, or neither. CAD and EAF Since 55° + 35° = 90°, CAD andEAF are complementary.

  33. D E C F B A Check It Out: Example 2C Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and EAF mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC andEAF are neither supplementary nor complementary.

  34. Additional Example 3: Finding Angle Measures Angles A and B are complementary. If mA is 56°, what is the mB? Since A and B are complementary, mA + mB = 90°. mA + mB = 90° 56° + mB = 90° Substitute 56° for mA. Subtract 56° from both sides. – 56° – 56° mB = 34° The measure of B = 34°.

  35. Check It Out: Example 3 Angles P and Q are supplementary. If mP is 32°, what is the mQ? Since P and Q are supplementary, mP + mQ = 180°. mP + mQ = 180° 32° + mQ = 180° Substitute 32° for mP. Subtract 32° from both sides.. – 32°– 32° mQ = 148° The measure of Q = 148°.

  36. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  37. 2. Lesson Quiz: Part I Tell whether each angle is acute, right, obtuse, or straight. straight 1. obtuse

  38. Lesson Quiz: Part II Use the diagram to tell whether the angles are complementary, supplementary, or neither. 3. AZB and BZC neither complementary 4. BZC and CZD 5. Angles M and N are supplementary. If mM is 117°, what is mN? 63°

  39. Lesson Quiz for Student Response Systems 1. Identify the type of the given angle. A. acute B. obtuse C. right D. straight

  40. Lesson Quiz for Student Response Systems 2. Identify the type of the given angle. A. acute B. obtuse C. right D. straight

  41. Lesson Quiz for Student Response Systems 3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD A. complementary B. supplementary C. right D. none

  42. Lesson Quiz for Student Response Systems 4. Angles A and B are complementary. If mA is 36°, what is mB? A.54° B.90° C.126° D.144°

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