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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 5-1 Points, Lines, Planes, and Angles Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Warm Up Solve. 1. x + 30 = x = x = = 61 + x 5. x + 20 = 90 Pre-Algebra 5-1 Points, Lines, Planes, and Angles x = 60 x = 77 x = 148 x = 29 x = 70

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Problem of the Day Mrs. Meyers class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyers class wants just cheese on the pizza?

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

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Vocabulary pointlineplane segmentrayangle rightiangleacuteiiangle obtuseiianglecomplementaryiiangles supplementaryiiangles vertical angles congruent

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles A point names a location. A Point A

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles A line is perfectly straight and extends forever in both directions. line l, or BC B C l

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles A plane is a perfectly flat surface that extends forever in all directions. plane P, or plane DEF D E F P

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles G H A segment, or line segment, is the part of a line between two points. GH

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles K J A ray is a part of a line that starts at one point and extends forever in one direction. KJ

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 1A & 1B: Naming Points, Lines, Planes, Segments, and Rays 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

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 1C: Naming Points, Lines, Planes, Segments, and Rays C. Name a plane in the figure. Plane, plane JKL Any 3 points in the plane that form a triangle can be used.

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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. KJ, KL, JK, LK JK, KL, LM, JM

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Try This: Example 1A & 1B 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.

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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: Example 1C

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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: Example 1D & 1E

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Pre-Algebra 5-1 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. m1 means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter X Y Z 1 m1 = 50°

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

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

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

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles A right angle can be labeled with a small box at the vertex. Reading Math

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 2A & 2B: Classifying Angles A. Name a right angle in the figure. B. Name two acute angles in the figure. TQS TQP, RQS

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 2C: Classifying Angles C. Name two obtuse angles in the figure. SQP, RQT

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 2D: Classifying Angles D. Name a pair of complementary angles. TQP, RQS mTQP + mRQS = 47° + 43° = 90°

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 2E: Classifying Angles E. Name two pairs of supplementary angles. TQP, RQT SQP, RQS mTQP + mRQT = 47° + 133° = 180° mSQP + mRQS = 137° + 43° = 180°

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles Try This: Example 2A A. Name a right angle in the figure. BEC E D C B A 90° 75° 15°

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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: Example 2B & 2C

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles D. Name a pair of complementary angles. AEB, CED E D C B A 90° 75° 15° Try This: Example 2D mAEB + mCED = 15° + 75° = 90°

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles E. Name two pairs of supplementary angles. AEB, BED CED, AEC E D C B A 90° 75° 15° Try This: Example 2D & 2E mAEB + mBED = 15° + 165° = 180° mCED + mAES = 75° + 105° = 180°

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

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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. A. If m1 = 37°, find m3. The measures of 1 and 2 add to 180° because they are supplementary, so m2 = 180° – 37° = 143°. The measures of 2 and 3 add to 180° because they are supplementary, so m3 = 180° – 143° = 37°.

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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. B. If m4 = y°, find m2. m 3 = 180° – y° m 2 = 180° – (180° – y°) = 180° – 180° + y° = y° Distributive Property m2 = m4

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. A. If m1 = 42°, find m3. 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° Try This: Example 3A

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. B. If m4 = x°, find m2. m 3 = 180° – x° m 2 = 180° – (180° – x°) = 180° –180° + x° = x° Distributive Property m2 = m Try This: Example 3B

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Pre-Algebra 5-1 Points, Lines, Planes, and Angles 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. 3. Name a right angle in the figure. 4. Name a pair of complementary angles. 5. If m1 47°, then find m3. 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

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