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8-1 Points, Lines, Planes, and Angles Common Core State Standards Learning Objective 7.G.5 Solve for an unknown angle using the “properties of angles.” Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Let’s Try Something New Today Holt Video Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Vocabulary point line segment ray right angle acute angle obtuse angle straight angle complementary angles supplementary angles Holt CA Course 1 plane angle 8-1 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. Holt CA Course 1 8-1 Points, Lines, Planes, and Angles A point names a location. Holt CA Course 1 •A Point A 8-1 Points, Lines, Planes, and Angles A line is perfectly straight and extends forever in both directions. Holt CA Course 1 l B C line l, or BC 8-1 Points, Lines, Planes, and Angles A plane is a perfectly flat surface that extends forever in all directions. Holt CA Course 1 P D E F plane P, or plane DEF 8-1 Points, Lines, Planes, and Angles A segment, or line segment, is the part of a line between two points. Holt CA Course 1 H G GH 8-1 Points, Lines, Planes, and Angles A ray is a part of a line that starts at one point and extends forever in K one direction. Holt CA Course 1 J KJ 8-1 Points, Lines, Planes, and Angles Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. A. a line Possible answers: KL or JK Holt CA Course 1 Any 2 points on a line can be used. 8-1 Points, Lines, Planes, and Angles Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. B. a plane Possible answers: Plane Holt CA Course 1 or plane JKL Any 3 points in the plane that form a triangle can name a plane. 8-1 Points, Lines, Planes, and Angles Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. C. four segments Possible answers: JK, KL, LM, JM D. four rays Possible answers: KJ, KL, JK, LK Holt CA Course 1 Write the two points in any order. Write the endpoint first. 8-1 Points, Lines, Planes, and Angles Caution! When naming a ray always write the endpoint first. Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Check It Out! Example 1 Use the diagram to name each figure. A A. four segments D B C Possible answers: AB, BC, CD, AD B. four rays Possible answers: CB, CD, DA, DC Holt CA Course 1 Write the two points in any order. Write the endpoint first. 8-1 Points, Lines, Planes, and Angles Check It Out! Example 1 Use the diagram to name each figure. A C. a line D B C Possible answers: AB or DC Holt CA Course 1 Any 2 points on a line can be used. 8-1 Points, Lines, Planes, and Angles Check It Out! Example 1 Use the diagram to name each figure. D. a plane A D Possible answers: Plane R or plane ABC Holt CA Course 1 B C Any 3 points in the plane that form a triangle can name a plane. 8-1 Points, Lines, Planes, and Angles Checking for Understanding Identify Ray Lines and Line Segments Points, Lines and Planes Lines, Line Segments & Rays Video Planes in Three Dimensions Video Holt CA Course 1 8-1 Points, Lines, Planes, and Angles An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex. Angles are usually measured in degrees ( °). Since ( 1 there are 360° in a circle, one degree is of a 360 circle. Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Additional Example 2: Classifying Angles Use the diagram to name each figure. A. a right angle TQS B. two acute angles TQP, RQS Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Reading Math mTQS is read as “the measure of angle TQS.” Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Additional Example 2: Classifying Angles Use the diagram to name each figure. C. two obtuse angles SQP, RQT Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Additional Example 2: Classifying Angles Use the diagram to name each figure. D. a pair of complementary angles TQP, RQS mTQP + m RQS = 47° + 43° = 90° Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Additional Example 2: Classifying Angles Use the diagram to name each figure. E. two pairs of supplementary angles TQP, RQT mTQP + m RQT = 47° + 133° = 180° SQP, SQR mSQP + m SQR = 137° + 43° = 180° Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Check It Out! Example 2 Use the diagram to name each figure. A. a right angle BEC C B A Holt CA Course 1 15° 90° E 75° D 8-1 Points, Lines, Planes, and Angles Check It Out! Example 2 Use the diagram to name each figure. B. two acute angles AEB, CED C. two obtuse angles BED, AEC C B A Holt CA Course 1 15° 90° E 75° D 8-1 Points, Lines, Planes, and Angles Check It Out! Example 2 Use the diagram to name each figure. D. a pair of complementary angles AEB, CED mAEB + m CED = 15° + 75° = 90° C B A Holt CA Course 1 15° 90° E 75° D 8-1 Points, Lines, Planes, and Angles Check It Out! Example 2 Use the diagram to name each figure. E. two pairs of supplementary angles AEB, BED mAEB + mBED = 15° + 165° = 180° CED, AEC mCED + mAEC = 75° + 105° = 180° C B A Holt CA Course 1 15° 90° E 75° D 8-1 Points, Lines, Planes, and Angles Lesson Quiz 1. Name two lines in the figure. Possible answer: AD and BE 2. Name a right angle in the figure. Possible answer: AGF 3. Name a pair of complementary angles. Possible answer: 1 and 2 Holt CA Course 1 8-1 Points, Lines, Planes, and Angles Classwork & Homework Lesson 8-1 Practice B Lesson 8-1 Problem Solving Holt CA Course 1