1. Pre-Algebra 5.1 Points, Lines, Planes, and Angles

2. 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 Warm Up

3. Learn to classify and name figures.

4. pointlineplane segmentrayangle rightiangleacuteiiangle obtuseiianglecomplementaryiiangles supplementaryiiangles vertical angles congruent Vocabulary

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

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

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

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

11. A. Name 4 points in the figure. B. Name a line in the figure. Point J, point K, Point L, and Point M Any 2 points on a line can be used. KL or JK Example

12. C. Name a plane in the figure. Plane, plane JKL Any 3 points in the plane that form a triangle can be used. Example

13. D. Name four segments in the figure. E. Name four rays in the figure. KJ, KL, JK, LK JK, KL, LM, JM Example

14. A. Name 4 points in the figure. B. Name a line in the figure. Point A, point B, Point C, and Point D A B C D DA or BC Any 2 points on a line can be used. Try This

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

16. D. Name four segments in the figure E. Name four rays in the figure DA, AD, BC, CB AB, BC, CD, DA A B C D Try This

17. 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. 1 360 X Y Z 1 m1 = 50°

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

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

20. 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°.

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

22. A. Name a right angle in the figure. B. Name two acute angles in the figure. TQS TQP, RQS Example

23. C. Name two obtuse angles in the figure. SQP, RQT Example

24. D. Name a pair of complementary angles. TQP, RQS mTQP + mRQS = 47° + 43° = 90° Example

25. E. Name two pairs of supplementary angles. TQP, RQT SQP, RQS mTQP + mRQT = 47° + 133° = 180° mSQP + mRQS = 137° + 43° = 180° Example

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

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

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

29. E. Name two pairs of supplementary angles. AEB, BED CED, AEC E D C B A 90° 75° 15° mAEB + mBED = 15° + 165° = 180° mCED + mAES = 75° + 105° = 180° Try This

30. 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.

31. 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°. Example

32. In the figure,  1 and  3 are vertical angles, and  2 and  4 are vertical angles. B. If m4 = y°, find m2. m  3 = 180° – y° m  2 = 180° – (180° – y°) = 180° – 180° + y° = y° Distributive Property m2 = m4 Example

33. In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. A. If m1 = 42°, find m3. 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°. 1 2 3 4 Try This

34. In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. B. If m4 = x°, find m2. m  3 = 180° – x° m  2 = 180° – (180° – x°) = 180° –180° + x° = x° Distributive Property m2 = m4 1 2 3 4 Try This

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