Notes: Identify Points, Lines, and Planes 1.1

Transcription

1 Notes: Identify Points, Lines, and Planes 1.1 Objective: Name and sketch geometric figures Write in words what each of the following symbols means. 1) PL 2) GD 3) M 4) KJ Name the following figures. 5) 6) 7) 8) 9) Name a pair of opposite rays in the following picture 10) Collinear points are points that. 11) Coplanar points are points that. Use the picture below for questions ) Give two other names for BD 13) Give another name for plane T 14) Name three points that are collinear. Then name a fourth point that is not collinear with those three points. 15) Name a point that is NOT coplanar with E, C, and A.

2 Use the picture below for questions Notes: Identify Points, Lines, and Planes ) Give another name for ST 17) Name all rays with endpoint Q 18) Name two pairs of opposite rays 19) Give another name for PR Use the picture below for questions ) Name the intersection of plane PQS and plane HGS. 21) Are points P and G collinear? Are they coplanar? 22) Sketch two lines that lie in a plane and intersect at one point. 23) Sketch two lines that lie in a plane, and one line that does not lie in the plane. You are given an equation of a line and a point. Use substitution to determine whether the point is on the line. 24) y x 4; A(5,1) 25) y 3x 4; A(7,1) Graph the inequality on a number line. Tell whether the graph is a segment, ray, point, or line. 26) x 3 27) x 7 or x 4

3 Notes: Use Segments and Congruence 1.2 Objective: Use segment postulates to identify congruent segments 1) XY means 2) XY means 3) Find RT 4) Find BC Plot the following points in a coordinate plane. Then determine whether the line segments named are congruent. 5) 6) Use the number line to find the indicated measure. 7) AB 8) CE 9) AE 10) BD

4 Notes: Use Segments and Congruence 1.2 In the diagram, points V, W, X, Y, and Z are collinear, VZ = 50, XZ = 22, and WX = XY = YZ. Find the indicated length. 11) WX 12) VW 13) WY 14) VX 15) WZ 16) VY 17) 18)

5 Notes: Use Midpoint and Distance Formulas 1.3 Objective: Find lengths of segments in the coordinate plane Midpoint Formula If A x 1, y ) and B x 2, y ) are two points in a coordinate plane, then the midpoint of AB is ( 1 ( 2 1) Find the midpoint of the segment graphed below. Find the coordinates of the midpoint of the segment with the given endpoints. 2) E(-7, -5) and F(-3, 7) 3) J(-8, -7) and K(11, 5) Use the given endpoint J and midpoint M of JK to find the coordinates of the other endpoint K. 4) J(1, 4), M(2, 1) 5) J(5, 1), M(1, 4) 6) J(6, -2), M(5, 3)

6 Notes: Use Midpoint and Distance Formulas 1.3 A midpoint. A segment bisector. A segment bisector can be a point, ray, line, line segment, or plane. Line bisects the segment. Find the indicated length. 7) Find RS 8) Find BC if AC = 19 cm 1 3 9) Find QR if PR = 9 in. 10) Find UW if VW = mm 2 8 In each diagram, M is the midpoint of the segment. Find the indicated length. 11) Find LN 12) Find AM

7 Notes: Use Midpoint and Distance Formulas 1.3 Distance Formula If A x 1, y ) and B x 2, y ) are two points in a coordinate plane, then the distance between A & B is ( 1 ( 2 **The distance between points A and B is the same as the length of the segment AB. Find the length of each segment. 13) 14) Find the distance between the following points (same as finding the length of the segment). 15) A(0, 2) and B(-3, 8) 16) C(-4, 2) and D(3, -7)

8 Notes: Measure and Classify Angles 1.4 Objective: Name, measure, and classify angles Write three names for the angle shown. Then name the vertex and sides of the angle. 1) 2) 3) Name three different angles in the diagram below. Give another name for the angle in the diagram below. Tell whether the angle appears to be acute, right, obtuse, or straight. 4) JKN 5) KMN 6) PQM 7) KLP Find the indicated angle measure. 8) m QST

9 Notes: Measure and Classify Angles 1.4 Use the given information to find the indicated angle measure. 9) Given m WXZ 80, find m YXZ Find the indicated angle measure. 10) a 11) b 12) c 13) d In each diagram, BD bisects ABC. Find m ABC. 14) 15)

10 Notes: Describe Angle Pair Relationships 1.5 Objective: Use special angle relationships to find angle measures Two angles are complementary angles if their measures add to. Two angles are supplementary angles if their measures add to. Two angles that share a common vertex and side are called. 1) Name a pair of complementary angles and a pair of supplementary angles. 1 and 2 are complementary angles. Given the measure of 1, find m 2 2) m ) m and 2 are supplementary angles. Given the measure of 1, find m 2 4) m ) m 1 32 Find 6) m ABC and m CBD. 7)

11 Notes: Describe Angle Pair Relationships and 2 are a. 3 and 6 are. Their measures. Their measures. Tell whether the angles are vertical angles, a linear pair, or neither. 8) 1 and 3 9) 5 and 8 10) 2 and 3 11) 4 and 9 12) 5 and 6 13) 6 and 7 14) Two angles form a linear pair. The measure of one angle is 3 times the measure of the other angle. Find the measure of each angle. Find the values of x and y. 15) 16)

12 Notes: Classify Polygons 1.6 Objective: Classify polygons A polygon is a closed figure with the following properties: It is formed by three or more line segments Each side intersects exactly 2 sides Tell whether the figure is a polygon and whether it is convex or concave. 1) 2) 3) 4) Equilateral: Equiangular: Regular: Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. 5) 6) 7)

13 Notes: Classify Polygons 1.6 8) The lengths of two sides of a regular pentagon are represented by the expressions 5x 27 and 2x 6. Find the length of a side of the pentagon. 9) The expressions ( 3x 63) and ( 7x 45) represent the measures of two angles of a regular decagon. Find the measure of an angle of the decagon. Each figure is a regular polygon. Expressions are given for two side lengths. Find the value of x. 10)

14 Notes: Find Perimeter, Circumference, and Area 1.7 Objective: Calculate dimensions of polygons Define the following terms on your vocabulary sheet: Perimeter, Circumference, Area, Diameter, Radius Find the perimeter (or circumference) and area of each figure Give your answers in terms of

15 5. Notes: Find Perimeter, Circumference, and Area 1.7 Find the perimeter of the figure. Round to the nearest tenth of a unit. 6. Use the information about the figure to find the indicated measure. 7. Area = 308 m Area = 264 ft Find the height h. Find the base b b 9. Perimeter = 31 in. Find the width w.