Geometry Unit1: Segment Relationships Notes Unit 1: Segment Relationships

[Pages:14]Geometry

Unit1: Segment Relationships

Unit 1: Segment Relationships

After completion of this unit, you will be able to...

? Name lines, rays, and segments ? Define and recognize the following relationships

o Midpoint o Segment Addition o Segment Bisector ? Use the relationships to find missing segment lengths

Notes

Timeline for Unit 1

Monday 26

Visualization Practice

Tuesday 27

Day 1 Naming Points, Lines, Rays, and

Segments

Wednesday 28

Day 2 Segment Relationships

2 No School

3

4

Day 4

Midpoint Formula

Review

Thursday 29

Day 2 Segment Relationships

Friday 30

Day 3 Distance Formula

5

6

Unit 1 Assessment

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Geometry

Unit1: Segment Relationships

Day 1 ? Naming Points, Lines, Segments, and Rays Notes

Notes

Term

Definition

Picture

Name

Point*

A point indicates location and has no size.

Line*

A line is represented by a straight path that extends in opposite directions without

an end.

Plane*

A plane is represented by a flat surface that extends without end.

Segment Ray

A segment is part of a line that consists of two

endpoints and all the points between them.

A ray is part of a line that consists of one endpoint and extends infinitely in the

other direction.

Opposite Rays

Opposite rays are two rays that share the same

endpoint and form a line.

Collinear

Points on the same line.

N/A

Coplanar

Points and lines that lie in the same plane.

*Undefined Term: Basic idea you use to build definitions for other figures

N/A 2

Geometry

Unit1: Segment Relationships

A postulate is an accepted statement of fact.

Postulate 1: Through any two points, there is exactly one line.

Postulate 2: If two distinct lines intersect, they intersect in exactly one point.

Postulate 3: If two distinct planes intersect, then they intersect in exactly one line.

Postulate 4: Through any three noncollinear points, there is exactly one plane.

Name the following in as many ways as possible:

1.

2.

3.

4. Use the figure at the right to answer the following questions: a. Are points F, B, and W collinear? b. Name the plane. c. Name 4 coplanar points. d. At what point does line and intersect?

Notes 3

Geometry Parallel

Unit1: Segment Relationships

Types of Lines

Intersecting

Notes Perpendicular

Lines that do not intersect.

ABintersect CD

Lines that intersect at a point.

AB CD

Lines that intersect at a 90 degree angle.

Draw and label a figure for each relationship: a. Point K lies on

b. and intersect at point E.

Day 1 ? Naming Points, Lines, and Planes Practice

1. Write the following using correct symbols:

2. Determine if the following are true or false. 4

Geometry 3. Find the intersection of:

Unit1: Segment Relationships

4. Determine the following:

Notes

5. Name the following:

a.

b.

c.

d.

e.

f.

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Geometry

Unit1: Segment Relationships

Notes

Day 2: Segment Relationships Notes

Think About It: See if you can determine the length of the requested segment. Draw a picture first.

1. C is between A and E. AC = 24 in and CE = 13 in. How long is AE?

2. C is between A and E. CE = 7 in and AE = 23 in. How long is AC?

Segment Addition Postulate: If point B is on, and between points A and C, then + =.

a. Use the diagram to find.

Segment Addition Given:

Conclusion:

b. Write an expression for AC.

c. Find the value of z.

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Geometry

Unit1: Segment Relationships

Midpoint: Point that divides the segment into two congruent segments.

a. Find and .

b. Find and.

Given:

Notes Midpoint

c. T is the midpoint of. Solve for x.

Conclusion:

Segment Bisector: A line, line segment, or ray that divides the line segment into two line segments of equal

length.

Segment Bisector

a. Find and .

Given:

b. Determine if you have enough information to determine if is the segment bisector of . Explain why or why not.

Conclusion:

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Geometry

Unit1: Segment Relationships

Day 2: Segment Relationships Practice

Find the measure of the stated segment.

1.

2.

3.

Notes

4.

5.

6.

7. If RS = TU, ST = 19, RU = 33 a) Find RS

b) Find SU.

8. In the diagram, points V, W, X, Y, and Z are collinear. VZ = 52, XZ= 20, and WX = XY = YZ. Find the indicated lengths.

a. WX

d. VW

b. VX

e. WZ

c. WY

f. VY

9. M is the midpoint of JL. Find JM.

10. Line l is the segment bisector of PQ . Solve for x.

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