Bellwork #1

1. Answer the following questions on your paper:a) What is slope-intercept form of a linear equation?b) What is point-slope form?c) What is standard form?

2. Draw a coordinate plane on your paper and label the following:a) x-axisb) y-axisc) Points: (0,1) ; (3,0) ; (2,-1) ; (-2, ½)d) A line with a slope of 1e) A line with a slope of -1

3. Find the least common multiple of:a) 4 and 20b) 2, 5, and 7c) 6 and 12

Bellwork #2

Solve each system of equations.

1. y = x + 5y = -x +7

2. y = 2x – 4

y = 4x – 10 3. y = 2x

y = -x +15

Copy the diagram below onto your own paper. How many different lines can you draw connecting pairs of points in the diagram?

• A

• B

• C

• D

TOOLS OF GEOMETRY

Unit 1

POINTS, L INES, AND PLANES

Section 1.1

Vocabulary Challenge

Write the above vocabulary words on your notes page.

Can you guess which vocabulary word goes with which definition?

AxiomCollinear

points

CoplanarLine

Plane

PointPostulate

Space

A single location that has no size.

POINT

A point is represented by a small dot and is named by a capital letter.

• A

• B

• C

• D• E

• F

A geometric figure is a set of points.

The set of all points.

SPACE

A series of points that extends in two opposite directions without

end.

LINE

You can name a line by any two points on the line, such as:A B

Read, “line AB”

Another way to name a line is with a single lowercase letter, such as line t.

t

Points that lie on the same line.

COLLINEAR POINTS

A B

Are points C,B, and A collinear?

Are points E, B, and D collinear?

Are points D, B, and A collinear?

What do you think: Are points C and E collinear?

Yes

Yes

No

A flat surface that has no thickness.

PLANE

You can name a plane by either a single capital letter or by at least three of its noncollinear points.

A plane contains many lines and extends without end in the directions of all its lines.

Points and lines in the same plane.

COPLANAR

Name the plane represented by the front of the ice cube.

plane AEFplane AEBplane ABFE

An accepted statement of fact.

POSTULATEOR AXIOM

What do you think: Are points C and E collinear?

Postulate 1-1

Through any two points there is exactly one line.

No more! No less!

A B

t

Line t is the only line that passes through points A and B.

What is one method to solve the following system of equations?

3x + 2y = 2y = 1/2x - 3

We can solve by graphing.

Why does graphing work to solve?

Postulate 1-2

If two lines intersect, then they intersect in exactly one point.

At what point do these two lines intersect?

Postulate 1-3

If two planes intersect, then they intersect in exactly one line.

What is the intersection of these two planes?

DC

What is the intersection of plane HGFE and plane BCGF? GF

Name two planes that intersect inBF plane BCFG and plane ABEF

Consider this three-legged music stand. A three-legged stand will always be stable. As long as the feet of the stand don’t lie in one line, the feet of the three legs will lie exactly in one plane.

Postulate 1-4

Through any three noncollinear points there is exactly one plane.

Copy this cube two times onto your own paper. (Be sure to label the vertices).

1. Shade the plane that contains A,B, and C. 2. Shade the plane that contains E, H, and C.

3. Name another point that is coplanar with points E, H, and C. Point B

Finding the least common multiple.

xyz

xyz

x2

yz

x2yz

x2yyz

x2yz

xxyxy2

xy2

yxyxz2

xyz2

zx3yz2

xyz2

xyxyxy2

xy2

y2

xyzxy4

xy4z