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## 5-1

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**5-1**Points, Lines, Planes, and Angles Warm Up Problem of the Day Lesson Presentation Course 3**5-1**Points, Lines, Planes, and Angles Course 3 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**5-1**Points, Lines, Planes, and Angles 1 3 1 6 Course 3 Problem of the Day Mrs. Meyer’s 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. Meyer’s class wants just cheese on the pizza?**5-1**Points, Lines, Planes, and Angles Course 3 Learn to classify and name figures.**5-1**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**5-1**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.**5-1**Points, Lines, Planes, and Angles Course 3 A point names a location. • A Point A**5-1**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.**5-1**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**5-1**Points, Lines, Planes, and Angles GH Course 3 A segment, or line segment, is the part of a line between two points. H G**5-1**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**5-1**Points, Lines, Planes, and Angles KL or JK Course 3 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.**5-1**Points, Lines, Planes, and Angles Plane , plane JKL Course 3 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.**5-1**Points, Lines, Planes, and Angles JK, KL, LM, JM KJ, KL, JK, LK Course 3 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.**5-1**Points, Lines, Planes, and Angles BC DA or Course 3 Try This: Example 1A & 1B 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**5-1**Points, Lines, Planes, and Angles Plane , plane ABC, plane BCD, plane CDA, or plane DAB Course 3 Try This: Example 1C C. Name a plane in the figure. Any 3 points in the plane that form a triangle can be used. B A C D**5-1**Points, Lines, Planes, and Angles AB, BC, CD, DA DA, AD, BC, CB Course 3 Try This: Example 1D & 1E D. Name four segments in the figure E. Name four rays in the figure B A C D**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 1 1 360 m1 = 50° Y Z Course 3**5-1**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°.**5-1**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°.**5-1**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°.**5-1**Points, Lines, Planes, and Angles Reading Math A right angle can be labeled with a small box at the vertex. Course 3**5-1**Points, Lines, Planes, and Angles Course 3 Additional Example 2A & 2B: Classifying Angles A. Name a right angle in the figure. TQS B. Name two acute angles in the figure. TQP, RQS**5-1**Points, Lines, Planes, and Angles Course 3 Additional Example 2C: Classifying Angles C. Name two obtuse angles in the figure. SQP, RQT**5-1**Points, Lines, Planes, and Angles Course 3 Additional Example 2D: Classifying Angles D. Name a pair of complementary angles. mTQP + mRQS = 47° + 43° = 90° TQP, RQS**5-1**Points, Lines, Planes, and Angles Course 3 Additional Example 2E: Classifying Angles E. Name two pairs of supplementary angles. TQP, RQT mTQP + mRQT = 47° + 133° = 180° mSQP + mRQS = 137° + 43° = 180° SQP, RQS**5-1**Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Try This: Example 2A A. Name a right angle in the figure. BEC**5-1**Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Try This: Example 2B & 2C B. Name two acute angles in the figure. AEB, CED C. Name two obtuse angles in the figure. BED, AEC**5-1**Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Try This: Example 2D D. Name a pair of complementary angles. mAEB + mCED = 15° + 75° = 90° AEB, CED**5-1**Points, Lines, Planes, and Angles C B 90° A D 75° 15° E Course 3 Try This: Example 2D & 2E E. Name two pairs of supplementary angles. mAEB + mBED = 15° + 165° = 180° AEB, BED mCED + mAEC = 75° + 105° = 180° CED, AEC**5-1**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.**5-1**Points, Lines, Planes, and Angles 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. 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°.**5-1**Points, Lines, Planes, and Angles 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. B. If mÐ4 = y°, find mÐ2. m3 = 180° – y° m2 = 180° – (180° – y°) = 180° – 180° + y° Distributive Property m2 = m4 = y°**5-1**Points, Lines, Planes, and Angles Course 3 Try This: Example 3A In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 A. If m1 = 42°, find m3. 1 4 The measures of 1 and 2 add to 180° because they are supplementary, so m2 = 180° – 42° = 138°. The measures of 2 and 3 add to 180° because they are supplementary, so m3 = 180° – 138° = 42°.**5-1**Points, Lines, Planes, and Angles Course 3 Try This: Example 3B In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 2 3 B. If m4 = x°, find m2. 1 4 m3 = 180° – x° m2 = 180° – (180° – x°) = 180° –180° + x° Distributive Property m2 = m4 = x°**5-1**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 m1 = 47°, then find m3. 47°