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Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x

5-1. Points, Lines, Planes, and Angles. Pre-Algebra. 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. Learn to classify and name figures. Vocabulary. point line plane

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Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x

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  1. 5-1 Points, Lines, Planes, and Angles Pre-Algebra 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

  2. Learn to classify and name figures.

  3. Vocabulary point line plane segment ray angle right angle acute angle obtuse angle complementary angles supplementary angles vertical angles congruent

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

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

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

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

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

  9. KL or JK Additional Example 1A & 1B: 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.

  10. Plane , plane JKL Additional Example 1C: 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.

  11. JK, KL, LM, JM KJ, KL, JK, LK Additional Example 1D & 1E: Naming Points, Lines, Planes, Segments, and Rays D. Name four segments in the figure. E. Name four rays in the figure.

  12. BC DA or Try This: Example 2A & 2B 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

  13. Plane , plane ABC, plane BCD, plane CDA, or plane DAB Try This: Example 2C C. Name a plane in the figure. Any 3 points in the plane that form a triangle can be used. B A C D

  14. AB, BC, CD, DA DA, AD, BC, CB Try This: Example 2D & 2E D. Name four segments in the figure E. Name four rays in the figure B A C D

  15. 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

  16. G H J F K The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.

  17. P N R Q M The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.

  18. 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°.

  19. Reading Math A right angle can be labeled with a small box at the vertex.

  20. Additional Example 3A & 3B: Classifying Angles A. Name a right angle in the figure. TQS B. Name two acute angles in the figure. TQP, RQS

  21. Additional Example 3C: Classifying Angles C. Name two obtuse angles in the figure. SQP, RQT

  22. Additional Example 3D: Classifying Angles D. Name a pair of complementary angles. mTQP + mRQS = 47° + 43° = 90° TQP, RQS

  23. Additional Example 3E: Classifying Angles E. Name two pairs of supplementary angles. TQP, RQT mTQP + mRQT = 47° + 133° = 180° mSQP + mRQS = 137° + 43° = 180° SQP, RQS

  24. C B 90° A D 75° 15° E Try This: Example 4A A. Name a right angle in the figure. BEC

  25. C B 90° A D 75° 15° E Try This: Example 4B & 4C B. Name two acute angles in the figure. AEB, CED C. Name two obtuse angles in the figure. BED, AEC

  26. C B 90° A D 75° 15° E Try This: Example 4D D. Name a pair of complementary angles. AEB, CED mAEB + mCED = 15° + 75° = 90°

  27. C B 90° A D 75° 15° E Try This: Example 4E 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

  28. 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.

  29. Additional Example 5A: Finding the Measure of Vertical Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. A. If m1 = 37°, find m3. The measures of 1 and 2 add to 180° because they are supplementary, so m2 = 180° – 37° = 143°. The measures of 2 and 3 add to 180° because they are supplementary, so m3 = 180° – 143° = 37°.

  30. Additional Example 5B: Finding the Measure of Vertical Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. B. If mÐ4 = y°, find mÐ2. m3 = 180° – y° m2 = 180° – (180° – y°) = 180° – 180° + y° Distributive Property m2 = m4 = y°

  31. Try This: Example 6A In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 A. If m1 = 42°, find m3. 1 4 The measures of 1 and 2 add to 180° because they are supplementary, so m2 = 180° – 42° = 138°. The measures of 2 and 3 add to 180° because they are supplementary, so m3 = 180° – 138° = 42°.

  32. Try This: Example 6B In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 B. 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°

  33. Possible answer: AD and BE 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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