Preparation for MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge. California Standards

Points, lines, and planes are the building blocks of geometry Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

A point names a location. Point A

A line is perfectly straight and extends forever in both directions. line l, or BC

A plane is a perfectly flat surface that extends forever in all directions. plane P, or plane DEF D F

A segment, or line segment, is the part of a line between two points. GH G

A ray is a part of a line that starts at one point and extends forever in one direction. J KJ K

Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. A. a line Possible answers: Any 2 points on a line can be used. KL or JK

Additional Example 1: Naming Lines, Planes, Segments, and Rays Use the diagram to name each figure. B. a plane Possible answers: Any 3 points in the plane that form a triangle can name a plane. Plane or plane JKL

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 Write the two points in any order. D. four rays Possible answers: Write the endpoint first. KJ, KL, JK, LK

When naming a ray always write the endpoint first. Caution!

Check It Out! Example 1 Use the diagram to name each figure. A B C D A. four segments Possible answers: AB, BC, CD, AD Write the two points in any order. B. four rays Possible answers: CB, CD, DA, DC Write the endpoint first.

Check It Out! Example 1 Use the diagram to name each figure. A B C D C. a line Possible answers: Any 2 points on a line can be used. AB or DC

Check It Out! Example 1 Use the diagram to name each figure. A B C D D. a plane Possible answers: Any 3 points in the plane that form a triangle can name a plane. Plane R or plane ABC

Angles are usually measured in degrees ((°). Since 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 there are 360° in a circle, one degree is of a circle. 1 360

Additional Example 2: Classifying Angles Use the diagram to name each figure. A. a right angle TQS B. two acute angles TQP, RQS

mTQS is read as “the measure of angle TQS.” Reading Math

Additional Example 2: Classifying Angles Use the diagram to name each figure. C. two obtuse angles SQP, RQT

Additional Example 2: Classifying Angles Use the diagram to name each figure. D. a pair of complementary angles TQP, RQS mTQP + m RQS = 47° + 43° = 90°

Additional Example 2: Classifying Angles Use the diagram to name each figure. E. two pairs of supplementary angles TQP, RQT mTQP + m RQT = 47° + 133° = 180° SQP, SQR mSQP + m SQR = 137° + 43° = 180°

Check It Out! Example 2 Use the diagram to name each figure. A. a right angle BEC E D C B A 90° 75° 15°

Check It Out! Example 2 Use the diagram to name each figure. B. two acute angles AEB, CED C. two obtuse angles BED, AEC E D C B A 90° 75° 15°

Check It Out! Example 2 Use the diagram to name each figure. D. a pair of complementary angles AEB, CED mAEB + m CED = 15° + 75° = 90° E D C B A 90° 75° 15°

Check It Out! Example 2 Use the diagram to name each figure. E. two pairs of supplementary angles AEB, BED mAEB + mBED = 15° + 165° = 180° CED, AEC mCED + mAEC = 75° + 105° = 180° E D C B A 90° 75° 15°