Chapter 1

Discovering Points, Lines, Planes, and Angles

Warm up1. If x=18 and y = 6, find the value of x – 4y2. What is the value of x + 3yz if x = 3, y = 6,

and z = 4?3. Determine if (-2,5) is a solution of 3x + 4y =

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

3 undefined terms of geometry - Point – has no dimension, A – point A

Line – has one dimension. Contains infinite # of points. line BC – BC or line Through any two points there is exactly one line.

l

A

BC

l

Plane – has two dimensions.Through any 3 points not on the same line, there is exactly one plane.

plane ABC or plane M

Coplanar – points in the same plane Noncoplanar – points not in the same

plane. Space – a boundless 3- D set of all

points

ABC

M

Lesson 1.1 Coordinate Plane

Collinear points – points that are on the same line

Noncollinear points – points that are not on the same line

A, B, C are collinear A, B, D are noncollinear

A BC

D

SOLUTION

EXAMPLE 1 Name points, lines, and planes

b. Name three points that are collinear.Name four points that are coplanar.

a. Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV.

a. Give two other names for PQ and for plane R.

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

ANSWER TS, PT; point V

1. Use the diagram. Give two other names for ST . Name a point that is not coplanar with points Q, S, and T.

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:

Line segment – a piece of a line, named using 2 endpoints.

AB - Segment AB AB – length of

segment AB

Ray – has one endpoint and continues in one direction.

CD – ray CD 2 rays that form

a line are called opposite rays

A

B

CD.

EXAMPLE 2 Name segments, rays, and opposite rays

b. 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 .

a. Give another name for GH .

Intersections The intersection of

2 lines is a point.

The intersection of a line and a plane is a point.

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.

Use the diagram at the right.

2. Name the intersection of PQ and line k.

ANSWER Point M

ANSWER

3. Name the intersection of plane A and plane B.

4. Name the intersection of line k and plane A.

Line k

Line k

Warm upDraw 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.