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California Standards

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.

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California Standards

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  1. 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.

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

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

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

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

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

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

  8. 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.

  9. 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.

  10. 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.

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

  12. 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.

  13. 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.

  14. 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

  15. 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.

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

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

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

  19. 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°

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

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