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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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**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**Vocabulary**point line plane segment ray angle right angle acute angle obtuse angle complementary angles supplementary angles vertical angles congruent**A point names a location.**• A Point A**C**l B line l, or BC A line is perfectly straight and extends forever in both directions.**A plane is a perfectly flat surface that extends forever in**all directions. P E plane P, or plane DEF D F**GH**A segment, or line segment, is the part of a line between two points. H G**A ray is a part of a line that starts at one point and**extends forever in one direction. J KJ K**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.**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.**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.**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**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**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**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**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°.**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°.**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°.**Reading Math**A right angle can be labeled with a small box at the vertex.**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**Additional Example 3C: Classifying Angles**C. Name two obtuse angles in the figure. SQP, RQT**Additional Example 3D: Classifying Angles**D. Name a pair of complementary angles. mTQP + mRQS = 47° + 43° = 90° TQP, RQS**Additional Example 3E: Classifying Angles**E. Name two pairs of supplementary angles. TQP, RQT mTQP + mRQT = 47° + 133° = 180° mSQP + mRQS = 137° + 43° = 180° SQP, RQS**C**B 90° A D 75° 15° E Try This: Example 4A A. Name a right angle in the figure. BEC**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**C**B 90° A D 75° 15° E Try This: Example 4D D. Name a pair of complementary angles. AEB, CED mAEB + mCED = 15° + 75° = 90°**C**B 90° A D 75° 15° E Try This: Example 4E E. Name two pairs of supplementary angles. mAEB + mBED = 15° + 165° = 180° AEB, BED mCED + mAEC = 75° + 105° = 180° CED, AEC**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.**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 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°.**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. m3 = 180° – y° m2 = 180° – (180° – y°) = 180° – 180° + y° Distributive Property m2 = m4 = y°**Try This: Example 6A**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°.**Try This: Example 6B**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°**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 m1 = 47°, then find m3. 47°

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