1.1 Points, Lines, and Planes

Name: ______Block:______Date: ______

Chapter 1

Essentialsof

Geometry

Sections Covered:

1.1 Points, Lines, and Planes

1.2 Segments and Congruence

1.3 Midpoint and Distance Formulas

1.4 Measure and Classify Angles

1.5 Angle Pair Relationships

The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include

a)investigating and using formulas for finding distance, midpoint, and slope;

Unit 2 Syllabus: Ch 1Essentials of Geometry

***Syllabus subject to change due to weather, pep rallies, illness, etc

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Mrs. Prusak are available in the morning. Email her to set up a time!

Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L409.

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Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons.

Notes 1.1Essential Definitions

DefinitionDiagramNotation

Intersection:

• The intersection of two lines is ______.
• The intersection of a line and a plane is ______.
• The intersection of two planes is ______.

Let’s put these definitions to use and you will be able to see that these really are not that difficult.

Name this line SEVEN different ways.

Using the same diagram to the right name

• FOUR rays:

• Opposite rays:

• Line segments:

Using the diagram to the right:

• Name the plane shaded in two different ways.

• Identify at least FOUR pairs of collinear points.

• Identify at a set of coplanar points.

• Where do lines g and h intersect?

• Where does line g intersect with plane F?

Notes 1.2 Segment Additional Postulate

Postulate:______

Theorem:______

Example:

Congruent Segments: segments that have the same ______.

a)AB  PQ is read "segment AB is ______to segment PQ."

b)AB = PQ is read "AB equals PQ" or “The length of segment AB equals the length of segment PQ.”

c)Since AB and PQ represent numbers, they are equal.

In contrast, AB and PQ represent figures and are called congruent.

Diagram:Notation:

Example:

Example:

Example: Together On Your Own

Example: Point S is between R and T on . Us e the given information to write an equation in terms of x. Solve the equation. Then, find RS and ST.

1. RS = 2x + 10b. RS = 3x – 16

ST = x – 4 ST = 4x – 8

RT = 21 RT = 2x + 36

Notes 1.3: Midpoint & Distance

Midpoint: ______

Segment bisector:______

1.) Find AC if AB = 10 cm.2.) Point W bisects. Find UV if WV = 14 inches.

3.) Find FM.4.) Point M is the midpoint of.

Find the length of.

PRACTICE: In the diagram, M is the midpoint of the segment. Find the indicated length.

a. b.

Ex1: Given two endpoints can you FIND THE MIDPOINT?

Find the coordinates of the midpoint of the segment with the given endpoints.

a. S (4, -1) and T (6, 0)b. L (4, 2) and P (0, 2) c. H (-5, 5) and K (7, 3)

Ex2: Given an endpoint and a midpoint, can you find the other endpoint?.

On Your Own:

Ex3: Given two endpoints, can you find the distance?

Find the length of the segment. Leave answer in simplest radical form and round to the nearest tenth of a unit.

Ex4: Given two endpoints, can you evaluate to see if they are congruent?

Notes 1.4: Angle Relationships

1. An angle is a figure formed by 2 ______that have the same endpoint.

2. The rays of the angle are called ______of the angle; the endpoint is called the ______.

An angle is named three ways:

1) by 3 capital letters, but the vertex must be in the middle.

______or ______

2) by a number placed inside the angle.

______

3) by the vertex...if there is only one angle with that vertex.

______

Adjacent angles are 2 angles that

1.

2.

3.

4.

Are these angles adjacent?

______

Definition: Congruent angles are angles that have the same ______.

Reminders…

TWO BIG IDEAS (for angles):

1. Angle Bisector Idea:

Ex. bisects ABC. Find the value of x.

Then find the measure of the angles to the nearest tenth.

On Your Own:

Find x given the following:

A. m∠ABC = 98°B. m∠ABC = 9x + 87°

2. Angle Addition Postulate:

EX:  ADC = 50°. What does ADB and  BDC equal to the nearest tenth?

Notes 1.5: Angle Relationships

Vertical Angles:

Linear Pair:

Adjacent:

Determine if the angles are vertical angles, linear pair, or neither.

a)

b)

c)

d)

e)

f) 5 and 6

g) 1 and 4

Classify the angles as linear pair, vertical angles or neither.

a)2, 5

b)4, 7

c)8, 10

d)3, 10

Find the value of each variable to the nearest tenth. Be sure to write an equation and circle the answer.

1. 2.

3.4.

Complementary Angles:

Supplementary Angles:

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1) Find the complement of 27.

2) Find the supplement of 115.

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3) The following angles are complementary. Find the measure of the angles to the nearest tenth.

4) The following angles are supplementary. Find the measure of the angles to the nearest tenth.

5) Two angles form a linear pair. The measure of one angle is 8 times the measure of the other angle. Find the measure of each angle to the nearest tenth.

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