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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x 5. x + 20 = 90. x = 60. x = 77. x = 148. x = 29. x = 70. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x 5. x + 20 = 90 x = 60 x = 77 x = 148 x = 29 x = 70

  3. California Standards Preparation for MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

  4. Vocabulary point line plane segment ray angle right angle acute angle obtuse angle straight angle complementary angles supplementary angles

  5. Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

  6. A point names a location. • A Point A

  7. C l B line l, or BC A line is perfectly straight and extends forever in both directions.

  8. A plane is a perfectly flat surface that extends forever in all directions. P E plane P, or plane DEF D F

  9. GH A segment, or line segment, is the part of a line between two points. H G

  10. A ray is a part of a line that starts at one point and extends forever in one direction. J KJ K

  11. KL or JK Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. A. a line Possible answers: Any 2 points on a line can be used.

  12. Plane or plane JKL Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. B. a plane Possible answers: Any 3 points in the plane that form a triangle can name a plane.

  13. JK, KL, LM, JM KJ, KL, JK, LK Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. C. four segments Possible answers: Write the two points in any order. D. four rays Possible answers: Write the endpoint first.

  14. Caution! When naming a ray always write the endpoint first.

  15. AB, BC, CD, AD B A C D CB, CD, DA, DC Check It Out! Example 1 Use the diagram to name each figure. A. four segments Possible answers: Write the two points in any order. B. four rays Possible answers: Write the endpoint first.

  16. B A AB or DC C D Check It Out! Example 1 Use the diagram to name each figure. C. a line Possible answers: Any 2 points on a line can be used.

  17. B A C D Check It Out! Example 1 Use the diagram to name each figure. D. a plane Possible answers: Any 3 points in the plane that form a triangle can name a plane. Plane R or plane ABC

  18. 1 360 An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex. Angles are usually measured in degrees ((°). Since there are 360° in a circle, one degree is of a circle.

  19. Additional Example 2: Classifying Angles Use the diagram to name each figure. A. a right angle TQS B. two acute angles TQP, RQS

  20. Reading Math mTQS is read as “the measure of angle TQS.”

  21. Additional Example 2: Classifying Angles Use the diagram to name each figure. C. two obtuse angles SQP, RQT

  22. Additional Example 2: Classifying Angles Use the diagram to name each figure. D. a pair of complementary angles TQP, RQS mTQP + mRQS = 47° + 43° = 90°

  23. Additional Example 2: Classifying Angles Use the diagram to name each figure. E. two pairs of supplementary angles TQP, RQT mTQP + mRQT = 47° + 133° = 180° mSQP + mSQR = 137° + 43° = 180° SQP, SQR

  24. C B 90° A D 75° 15° E Check It Out! Example 2 Use the diagram to name each figure. A. a right angle BEC

  25. C B 90° A D 75° 15° E Check It Out! Example 2 Use the diagram to name each figure. B. two acute angles AEB, CED C. two obtuse angles BED, AEC

  26. C B 90° A D 75° 15° E Check It Out! Example 2 Use the diagram to name each figure. D. a pair of complementary angles mAEB + mCED = 15° + 75° = 90° AEB, CED

  27. C B 90° A D 75° 15° E Check It Out! Example 2 Use the diagram to name each figure. E. two pairs of supplementary angles mAEB + mBED = 15° + 165° = 180° AEB, BED mCED + mAEC = 75° + 105° = 180° CED, AEC

  28. Possible answer: AD and BE Lesson Quiz 1. Name two lines in the figure. 2. Name a right angle in the figure. Possible answer: AGF 3. Name a pair of complementary angles. Possible answer: 1 and 2

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