GEOMETRY - Yonkers Public Schools

[Pages:62]GEOMETRY

Unit 1

Points, Planes, & Lines

Prepared by: G. Alvarez-Garcia, S. George, & R. Mercadante

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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1.1

Points, Lines, and Planes

Definition

A point has no ________________.

The "easy" definition

What does it look like?

How is it written?

A line extends in _______ dimension.

A plane extends in _______ dimensions.

A line segment AB consists of ____________ A and B, and all the points on line AB that are ________________ A and B.

A ray AB consists of the initial point ____ and all the points on the line AB that lie on _____________ __________ of A as point B.

THINK ABOUT IT!

Is there a difference between lines and ?

Is there difference between and ?

Example 1: 1.

C

Give all the naEmes ofFthe figures shown below.

2.

3.

D

F

E

I

G

J

4.

J

O P

5.

P QR

F E

6. MN

O P

J

O

Geometry CC RHS

Unit 1OPoPints, Planes, & Lines

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J

I

G

Example 2: Name segments and rays. a. Give another name for .

H

b. True or false: and are the same line.

c. and ____ are the same rays.

d. Name all the points given on . Postulate

Theorem

?J J

When points are created

by intersection s of lines,

U is between L and V

The Name

vs.

A

B

6 in

Its Measure

SEGMENT ADDITION POSTULATE

If B is between A and C,

then _______________________.

LIL + LIL = BIG

_____+______=______

Example 1: Draw a diagram and write the word form.

1. I is between J and M.

2. T is between A and E.

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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Example 2: Using Segment Addition Postulate

1. a) O is between M and P. Find the length of

if

and PO = 14.

2. E is be between N and T. If

and

, find the length of and explain.

b) What would your reasoning be if asked to explain why you set up the equation above?

3. Y is be between X and Z. If

and

find the length of and explain.

N E T

4. A is be between H and T. If

,

, and

, solve for . Explain.

H

A

T

5. I is be between K and D. If

,

, and

, find . Explain.

6. G is be between P and A. If

,

, and

, solve for . Explain.

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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Regents Test

Basic Concepts and Definitions

Questions 1 through 9 refer to the following: 1) PR and TS determine a plane. TRUE FALSE 2) Points T, Q, and S are collinear. TRUE FALSE 3) S is between P and R. TRUE FALSE 4) Points P, Q, and R are collinear. TRUE FALSE 5) PR and TS intersect at Q. TRUE FALSE 6) Points T, Q, and S are non-collinear. TRUE FALSE 7) Points P, Q, and T are non-collinear. TRUE FALSE 8) Q is between P and R. TRUE FALSE 9) Points S, Q, and R are collinear. TRUE FALSE Questions 10 through 16 refer to the following: In the diagram below, points P, N, and Q are collinear. Indicate whether the given statement is True or False.

10) Points M, N, K and Q are coplanar. TRUE FALSE 11) Points P, K, and Q determine a plane. TRUE FALSE 12) Only one plane contains points P, N, and Q. TRUE FALSE

13) PQ and NK intersect at N. TRUE FALSE

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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14) Points N, K, and M determine a plane. 15) KN and M determine a plane. TRUE

TRUE FALSE

FALSE

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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16) Points P, K, N, and Q are coplanar. TRUE FALSE 17) If two planes intersect, then their intersection is a line. TRUE 18) PQ has no endpoints. TRUE FALSE 19) PQ has only one endpoint. TRUE FALSE 20) A line segment has exactly one midpoint. TRUE FALSE 21) Tell whether a point, a line, or a plane is illustrated by

FALSE .

22) Tell whether a point, a line, or a plane is illustrated by .

23) PQ has no endpoints. TRUE FALSE 24) FG has only one endpoint. TRUE FALSE 25) PQ has two endpoints. TRUE FALSE 26) Tell whether a point, a line, or a plane is illustrated by the top of a desk.

1900 - 1 - Page 2

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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27) If two lines intersect, then their intersection is a point. TRUE FALSE 28) It is possible to define each geometric term by using previously defined geometric terms. TRUE 29) AB has no endpoints. TRUE FALSE 30) Another name for PQ is QP. TRUE FALSE 31) Tell whether a point, a line, or a plane is illustrated by the tip of a pen.

FALSE

32) Tell whether a point, a line, or a plane is illustrated by the edge of a textbook.

33) CD has two endpoints. TRUE FALSE 34) Tell whether a point, a line or a plane is illustrated by a basketball backboard.

35) Another name for PQ is QP. TRUE FALSE 36) PQ has two endpoints. TRUE FALSE

Geometry CC RHS

Unit 1 Points, Planes, & Lines

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