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7-1. Points, Lines, Planes, and Angles. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 7-1. Points, Lines, Planes, and Angles. Course 3. Learn to classify and name figures. 7-1. Points, Lines, Planes, and Angles. Course 3. Insert Lesson Title Here. Vocabulary.

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  1. 7-1 Points, Lines, Planes, and Angles Warm Up Problem of the Day Lesson Presentation Course 3

  2. 7-1 Points, Lines, Planes, and Angles Course 3 Learn to classify and name figures.

  3. 7-1 Points, Lines, Planes, and Angles Course 3 Insert Lesson Title Here Vocabulary point line plane segment ray angle right angle acute angle obtuse angle complementary angles supplementary angles vertical angles congruent

  4. 7-1 Points, Lines, Planes, and Angles Course 3 Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

  5. 7-1 Points, Lines, Planes, and Angles Course 3 A point names a location. • A Point A

  6. 7-1 Points, Lines, Planes, and Angles C l B line l, or BC Course 3 A line is perfectly straight and extends forever in both directions.

  7. 7-1 Points, Lines, Planes, and Angles Course 3 A plane is a perfectly flat surface that extends forever in all directions. P E plane P, or plane DEF D F

  8. 7-1 Points, Lines, Planes, and Angles GH Course 3 A segment, or line segment, is the part of a line between two points. H G

  9. 7-1 Points, Lines, Planes, and Angles Course 3 A ray is a part of a line that starts at one point and extends forever in one direction. J KJ K

  10. 7-1 Points, Lines, Planes, and Angles KL or JK Course 3 Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays A. Name 4 points in the figure. Point J, point K, point L, and point M B. Name a line in the figure. Any 2 points on a line can be used.

  11. 7-1 Points, Lines, Planes, and Angles Plane , plane JKL Course 3 Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays C. Name a plane in the figure. Any 3 points in the plane that form a triangle can be used.

  12. 7-1 Points, Lines, Planes, and Angles JK, KL, LM, JM KJ, KL, JK, LK Course 3 Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays D. Name four segments in the figure. E. Name four rays in the figure.

  13. 7-1 Points, Lines, Planes, and Angles BC DA or Course 3 Check It Out: Example 1 A. Name 4 points in the figure. Point A, point B, point C, and point D B. Name a line in the figure. Any 2 points on a line can be used. B A C D

  14. 7-1 Points, Lines, Planes, and Angles Plane , plane ABC, plane BCD, plane CDA, or plane DAB Course 3 Check It Out: Example 1 C. Name a plane in the figure. Any 3 points in the plane that form a triangle can be used. B A C D

  15. 7-1 Points, Lines, Planes, and Angles AB, BC, CD, DA DA, AD, BC, CB Course 3 Check It Out: Example 1 D. Name four segments in the figure E. Name four rays in the figure B A C D

  16. 7-1 Points, Lines, Planes, and Angles An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees. One degree, or 1°, is of a circle. m1 means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter. X 1 1 360 m1 = 50° Y Z Course 3

  17. 7-1 Points, Lines, Planes, and Angles G H J F K Course 3 The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.

  18. 7-1 Points, Lines, Planes, and Angles P N R Q M Course 3 The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.

  19. 7-1 Points, Lines, Planes, and Angles Course 3 A right angle measures 90°. An acute angle measures less than 90°. An obtuse angle measures greater than 90° and less than 180°. Complementary angles have measures that add to 90°. Supplementary angles have measures that add to 180°.

  20. 7-1 Points, Lines, Planes, and Angles Reading Math A right angle can be labeled with a small box at the vertex. Course 3

  21. 7-1 Points, Lines, Planes, and Angles Course 3 Additional Example 2: Classifying Angles A. Name a right angle in the figure. TQS B. Name two acute angles in the figure. TQP, RQS

  22. 7-1 Points, Lines, Planes, and Angles Course 3 Additional Example 2: Classifying Angles C. Name two obtuse angles in the figure. SQP, RQT

  23. 7-1 Points, Lines, Planes, and Angles Course 3 Additional Example 2: Classifying Angles D. Name a pair of complementary angles. mTQP + mRQS = 47° + 43° = 90° TQP, RQS

  24. 7-1 Points, Lines, Planes, and Angles Course 3 Additional Example 2: Classifying Angles E. Name two pairs of supplementary angles. TQP, RQT mTQP + mRQT = 47° + 133° = 180° mSQP + mSQR = 137° + 43° = 180° SQP, SQR

  25. 7-1 Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Check It Out: Example 2 A. Name a right angle in the figure. BEC

  26. 7-1 Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Check It Out: Example 2 B. Name two acute angles in the figure. AEB, CED C. Name two obtuse angles in the figure. BED, AEC

  27. 7-1 Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Check It Out: Example 2 D. Name a pair of complementary angles. mAEB + mCED = 15° + 75° = 90° AEB, CED

  28. 7-1 Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Check It Out: Example 2 E. Name two pairs of supplementary angles. mAEB + mBED = 15° + 165° = 180° AEB, BED mCED + mAEC = 75° + 105° = 180° CED, AEC

  29. 7-1 Points, Lines, Planes, and Angles Course 3 • Congruent figures have the same size and shape. • Segments that have the same length are congruent. • Angles that have the same measure are congruent. • The symbol for congruence is , which is read “is congruent to.” • Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.

  30. 7-1 Points, Lines, Planes, and Angles ~ So m1 = m3 or m1 = m3. Course 3 Additional Example 3A: Finding the Measure of Vertical Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. If m1 = 37°, find m3. The measures of 1 and 2 are supplementary. m2 = 180° – 37° = 143° The measures of 2 and 3 are supplementary. m3 = 180° – 143° = 37°

  31. 7-1 Points, Lines, Planes, and Angles So m4 = m2 or m4  m2. Course 3 Additional Example 3B: Finding the Measure of Vertical Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. If m4 = y°, find m2. m3 = 180° – y° m2 = 180° – (180° – y°) = 180° – 180° + y° Distributive Property m2 = m4 = y°

  32. 7-1 Points, Lines, Planes, and Angles So m1 = m3 or m1  m3. Course 3 Check It Out: Example 3A In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 If m1 = 42°, find m3. 1 4 The measures of 1 and 2 are supplementary. m2 = 180° – 42° = 138° The measures of 2 and 3 are supplementary. m3 = 180° – 138° = 42°

  33. 7-1 Points, Lines, Planes, and Angles So m4 = m2 or m4  m2. Course 3 Check It Out: Example 3B In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 If m4 = x°, find m2. 1 4 m3 = 180° – x° m2 = 180° – (180° – x°) = 180° –180° + x° Distributive Property m2 = m4 = x°

  34. 7-1 Points, Lines, Planes, and Angles Possible answer: AD and BE Course 3 Lesson Quiz In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 1. Name three points in the figure. Possible answer: A, B, and C 2. Name two lines in the figure. 3. Name a right angle in the figure. Possible answer: AGF 4. Name a pair of complementary angles. Possible answer: 1 and 2 5. If m1 = 47°, then find m3. 47°

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