Chapter 1 Student Notes

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Chapter 1 TestTuesday, August 29th

1.1 Points, Lines and Planes

Point -

Line -

Collinear -

• T / F A and B are Collinear• T / F A and C are Collinear• T / F A, B and C are Collinear

Plane -

Coplanar -A B

• Name 3 Coplanar Points ________

•Name 3 Noncoplanar Points _________

• T/F C, D and G are coplanar

• T/F A, B, E, F are coplanar

• T/F A, B, C, E are coplanar

Draw and Label each of the following1. n and m intersect at P

2. p contains N

3. P contains A and B, but not C

Draw and Label each of the following4. m intersects P at X

5. P and R intersect at m

1.2Segments

Objective:1) Learn the language of Geometry2) Become familiar with segments and segment

measure

Line Segment -

Betweenness of Points -

Measure of a Segment -

Segment Congruence -

Segment Congruence is marked on a figure in the following

manner.

Multiple Pairs of Congruent Segments

From the markings on the above figure, make 2 congruence statement.CB

1. AC = 4, AD = 3, Find CD = ______

2. CD = 15, AD = 7, Find AC = _____

A is between C and D. Find Each Measure.

C 4 A 3 D

C A 7 D

3. AC = x + 1, AD = x + 3, CD = 3x – 5, Find x = _____

C x + 1 A x + 3 D

3x - 5

1. AC = 8, AD = 5, Find CD = ______

2. CD = 20, AD = 12, Find AC = _____

C 8 A 5 D

C A 12 D

3. AC = 2x + 1, AD = 2x + 3, CD = 5x – 10, Find x = ___

C 2x + 1 A 2x + 3 D

5x – 10

C is between A and B in each figure. Select the figure that has AB = 12. Select all that apply.

A 8 C 4 B D 8 B A

A. C is between A and B. B. B is between A and D.

C. B is between A and D.AB = 2x + 5, BD = 3x + 4, AD = 6x – 3

D. B is between A and D.AB = 2x + 2, DB = 4x +2, DA =34

Answer: ____________

1.3Distance and Midpoint

Distance on a Number Line =

A B C D

-5 0 5

Use the number line to find the length of each segment.

Distance on a Coordinate Plane

A(2, 2)B(-4, 1)

C(2, -4)

Find the length of each segment.

DistanceFormula

A(2, 2)B(-4, 1)

C(2, -4)

Find the length of each segment.

Midpoint on a Number Line

Midpoint =

A B C D

-5 0 5

Find the midpoint of each segment.

A B C D

-5 0 5

4. If A is the midpoint of EC, what is the location for point E?

Midpoint on a Coordinate Plane

A(2, 2)B(-4, 1)

C(2, -4)

Midpoint = ( )x1 + x2 , y1 + y2

2 2Find the midpoint of each segment.

= ( ) = ( )

A(2, 2)B(-4, 1)

C(2, -4)

= ( ) = ( )

A(2, 2)B(-4, 1)

C(2, -4)

= ( ) = ( )

M is the midpoint of AB. Given the following information, find the missing coordinates.

M(2, 6) , B(12, 10) , A ( ? , ? ) Midpoint = ( )x1 + x2 , y1 + y2

M is the midpoint of AB. Given the following information, find the missing coordinates.

M(6, -8) , A(2, 0) , B ( ? , ? ) Midpoint = ( )x1 + x2 , y1 + y2

1.4Angle Measure

Angle–

Angles and Points

Points _______________________________

G ____________________

H ____________________

E ____________________H

Naming Angles

1. ________

2. ________

3. ________

4. ________

Name the angle at the right as many ways as possible.

Naming Angles

Name the angles at the right as many ways as possible.

1. _______

2. _______

3. _______

4. _______

1. _______

2. _______

3. _______

4. _______

Naming Angles

Name the angles at the right as many ways as possible.

1. _________

2. _________

3. _________

●●● ●

●●

There is more than one angle at vertex K, __________________ ____________________________________

Types of Angles

Right angle:

________ different types of angles:

Acute angle:

Types of Angles

Obtuse angle: Straight angle:

Can also be called __________ ________________.

Congruent Angles

Multiple Sets of Congruent Angles

__________

KM is an angle bisector.

Angle Bisector

What conclusion can you draw about the figure at the right?

_________________or

________________

When you want to add angles, use ______________________ _____________________________________________________________..

If you add m1 + m2, what is your result?_____________________________.

Adding Angles

●●●

L28o48o

Angle Addition Postulate The sum of the two smaller angles adjacent angles will

_______________________________________________________________________________________________.

Complete:

m ______ + m ______ = m _______

orm ______ + m ______ = m _______

Draw your own diagram and answer this question:

If ML is an angle bisector of PMY and mPML = 87, then find:

mPMY = _______mLMY = _______

Example

JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4. Find x and mLJM.

K(4x + 10)o

(6x – 4)o

mLJM = _____

RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3. Find x and mPRS.

(4x + 3)o

mPRS = ___

1-5Angle Pairs

Complementary Angles -

Examples:

Perpendicular – _______________________

Supplementary Angles-

Examples:

Adjacent Angles

Vertical Angles-

Example:

Theorem:

●●● A

What’s “Important” in Geometry?4 things to always look for !

. . . and ___________( )Most of the rules (theorems)and vocabulary of Geometryare based on these 4 things.

Examples1. 1 & 2 are complementary. m1 = 4x + 5,

m2 = 5x + 4. Find x and the measure of each angle. x = _____

m1 = _____

m2 = _____

Examples

2. 5 & 6 are supplementary. m5 = 10x + 12,

m6 = 2x + 6. Find x and the measure of each angle.

x = _____

m5 = _____

m6 = _____

Examples

3. m1 = 2x + 7, m3 = 3x – 3. Find x and the measure of each angle.

Find x = _____

m 2 = _____

m1 = _____

Examples4. m2 = 5x + 12, m4 = 7x – 20. Find x and the measure of each angle.

x = _____

m 2 = _____

m1 = _____

1.6Polygons

Determine if each figure is a polgyon

Polygon -

Example of Concave PolygonsConcave Polgons

Examples of Convex Polygons

Convex Polygons

Number of Sides3456789

10111213n

Name of Polygon Hint

Examples of Regular Polygons

Regular Polygon-

Find the perimeter of each polygon.

Perimeter - distance around a polygon

Square RectangleRegular Hexagon

P = _______

P = ______

P = ________

Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.

Find the perimeter and area of the polygon below.

5cm5cm

P = ________

A = ________

1. A(-3, 0), B(0, 4), C(4, -3)

Triangle ABC has the following coordinates. Find the perimeter of ABC.

P = _______

Chapter 1 Student Notes

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