Name: _________________________________Block:_____________Date: ____________________

Chapter 1 Essentials of

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

Unit 2 Syllabus: Ch 1 Essentials of Geometry Bloc Dat Topic Homework

SOL G.3

k e7 9/22 1.1Identify Points, Lines, and Planes

1.2Use Segments and CongruenceWkst: 1.1 Definitions and 1.2 Segment Addition Postulate

8 9/24 1.3 Use Midpoint and Distance Formulas

Wkst: 1.3 Midpoint and Distance

9 9/26 Review Day Wkst: 1.1-1.3 Review 10 9/30 Quiz 1.1-1.3 Spiral Review11 10/2 1.4 Measure and Classify Angles Wkst: 1.4 Angle Measurement12 10/4 1.5 Describe Angle Pair Relationships Wkst: 1.5 Angle Relationships13 10/6 Review Day Wkst: Chapter 1 Review 14 10/8 Chapter 1 Test Spiral Review

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

Need Help?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.

Need to make up a test/quiz?Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons.

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Notes 1.1 Essential Definitions Definition Diagram Notation

1. PointNo dimension

2. LineOne dimension; extends without end

3. PlaneTwo dimensions; extends without end

4. Line SegmentPart of a line that contains two endpoints and all the points between them

5. RayPart of line that consists of the endpoint and all the points on the line that extend in one direction Initial pointBeginning point of the ray

6. Opposite RaysRays with same initial point and extend to form a line

7. Collinear pointsPoints that lie on the same line

8. Coplanar pointsPoints that lie on the same plane

Intersection:

3

A

A B

C

A

AB

C

X Y

XY

ZM

lR S

XY

ZM

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?

4

AC

m

B

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:

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Segment Addition Postulate: If ________ is between ________ and ________, then

__________ + __________ = ___________.

Remember: “The ____________ is equal to the ___________________________.”

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.

a. RS = 2x + 10 b. RS = 3x – 16

ST = x – 4 ST = 4x – 8 RT = 21 RT = 2x + 36

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Notes 1.3: Midpoint & Distance

Midpoint: _______________________________________________________________________________

Segment bisector:_________________________________________________________________________

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

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Use the given endpoint R and midpoint M of RS to find the coordinates of the endpoint S. R (1, 2) and M (-2, 1)**Think…. DMSE

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:

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The coordinates of a segment’s midpoint are

(______________, ________________)

**Think SAD….. The endpoints of are A(3, 2) and B(6, 7). Find the coordinates of the midpoint M.

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?

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Think… Pythagorean Thm

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 that1. 2.3.4.

Are these angles adjacent?

________ ________ ________ _______ _______

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

Reminders…

1. Acute angle- angle with measure between _____ and _____.

2. Right angle- angle with measure of _______.

3. Obtuse angle- angle with measure between _____ and ______.

4. Straight angle- angle with measure of _________.

10

1 2 3

45

6

7

8

910

CB

A

2

Even though the angle is named four different ways, it is the same angle.

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°

11

T

A

C

B

(3X + 13)

(5X - 17)

2. Angle Addition Postulate:

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

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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 6g) 1 and 4

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

a) 2, 5b) 4, 7c) 8, 10d) 3, 10

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

1. 2.

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3. 4.

Complementary Angles:

Supplementary Angles:

1) Find the complement of 27. 2) Find the supplement of 115.

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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