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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 Slide 2 Pre-Algebra 5-1 Points, Lines, Planes, and Angles Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 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 Slide 3 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? 1616 1313 Slide 4 Pre-Algebra 5-1 Points, Lines, Planes, and Angles Learn to classify and name figures. Slide 5 Pre-Algebra 5-1 Points, Lines, Planes, and Angles Vocabulary pointlineplane segmentrayangle rightiangleacuteiiangle obtuseiianglecomplementaryiiangles supplementaryiiangles vertical angles congruent Slide 6 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. Slide 7 Pre-Algebra 5-1 Points, Lines, Planes, and Angles A point names a location. A Point A Slide 8 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 Slide 9 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 Slide 10 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 Slide 11 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 Slide 12 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 Slide 13 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. Slide 14 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 Slide 15 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. Slide 16 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 Slide 17 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 Slide 18 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. 1 360 X Y Z 1 m1 = 50 Slide 19 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 Slide 20 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 Slide 21 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. Slide 22 Pre-Algebra 5-1 Points, Lines, Planes, and Angles A right angle can be labeled with a small box at the vertex. Reading Math Slide 23 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 Slide 24 Pre-Algebra 5-1 Points, Lines, Planes, and Angles Additional Example 2C: Classifying Angles C. Name two obtuse angles in the figure. SQP, RQT Slide 25 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 Slide 26 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 Slide 27 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 Slide 28 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 Slide 29 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 Slide 30 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 Slide 31 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. Slide 32 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. Slide 33 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 Slide 34 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. 1 2 3 4 Try This: Example 3A Slide 35 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 = m4 1 2 3 4 Try This: Example 3B Slide 36 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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