Chapter 1 Discovering Points Lines Planes and Angles

Chapter 1 Discovering Points, Lines, Planes, and Angles

Warm up 1. If x=18 and y = 6, find the value of x – 4 y 2. What is the value of x + 3 yz if x = 3, y = 6, and z = 4? 3. Determine if (-2, 5) is a solution of 3 x + 4 y = 14. 4. The formula for acceleration is a = (f –s)/t, where a is acceleration, f is final velocity and t is time. Find the starting velocity, s, of a train that accelerated at a rate of 1. 4 meters per second to a velocity of 6. 8 meters per second in 4 seconds.

Lesson 1. 1 Points, Lines, and Planes o 3 undefined terms of geometry o Point – has no dimension, A – point A o Line – has one dimension. C B Contains infinite # of points. line BC – BC or line l Through any two points there is exactly one line. l A

o Plane – has two dimensions. Through any 3 points not on the same line, there is exactly one plane ABC or plane M M C A B o Coplanar – points in the same plane o Noncoplanar – points not in the same plane. o Space – a boundless 3 - D set of all points

Lesson 1. 1 Coordinate Plane o Collinear points – points that are on the same line o Noncollinear points – points that are not on the same line A, B, C are C A B collinear D A, B, D are noncollinear

EXAMPLE 1 Name points, lines, and planes a. Give two other names for PQ and for plane R. b. Name three points that are collinear. Name four points that are coplanar. SOLUTION a. Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV. b. Points S, P, and T lie on the same line, so they are collinear. Points S, P, T, and V lie in the same plane, so they are coplanar.

Warm-Up 1. Use the diagram. Give two other names for ST. Name a point that is not coplanar with points Q, S, and T. ANSWER TS, PT; point V 2. Name 3 collinear points. 3. Name 3 noncollinear points. 4. Give another name for plane R. 5. Does Q lie in plane R? 6. Name 4 noncoplanar points. (Different from #1)

Defined Terms: o Ray – has one o Line segment – a endpoint and piece of a line, continues in one named using 2 direction. B endpoints. . A o AB - Segment AB o AB – length of segment AB C D o CD – ray CD o 2 rays that form a line are called opposite rays

EXAMPLE 2 a. b. Name segments, rays, and opposite rays Give another name for GH. Name all rays with endpoint J. Which of these rays are opposite rays? SOLUTION a. Another name for GH is HG. b. The rays with endpoint J are JE , JG , JF , and JH. The pairs of opposite rays with endpoint J are JE and JF , and JG and JH.

Intersections o The intersection of 2 lines is a point. o The intersection of a line and a plane is a point. o The intersection of 2 planes is a line.

GUIDED PRACTICE for Examples 3 and 4 1. Sketch two different lines that intersect a plane at the same point. ANSWER Use the diagram at the right. 2. Name the intersection of PQ and line k. Point M ANSWER 3. 4. Name the intersection of plane A and plane B. Line k Name the intersection of line k and plane A. Line k

Warm up Draw a diagram 1. R, S, and T are collinear. X is not collinear. 2. AB and QR intersect at point D. 3. M is between N and O. P is between M and N. 4. Lines j and k intersect at point C and are not in plane M, but point C is in plane M.

Warm-Up 1. Name the intersection of the two planes. 2. Name the intersection of plane GFD and line BC 3. Name 3 collinear points. 4. Name 4 noncoplanar points.