1.1: _________________________________________________ Date: __________

Geometry

A __________ is a two-dimensional diagram that you can _______ a three-dimensional figure. A net

shows _____ of the surfaces of a figure in one view.

Ex 1). Circle the net that you can NOT fold into a cube.

Ex 2). Suppose you fold the net into a cube. What color will be opposite each face?

a) red: _____________________

b) blue: ____________________

c) green: ____________________

Ex 3). Suppose you fold the net into a cube. Which color is missing from each side?

a) b) c)

__________________ __________________ __________________

Ex 4). The net below folds into a cube. Which letters will be on the top and front of the cube?

Top: _______ Front: ________

Ex 5). What is a net for the cereal box below? Label the net with its dimensions.

a) b)

Homework: pg. 6 #1, 2, 5 – 10, 17 – 20, 22 – 25, 27, 28, contract & supplies check on Monday

1.2 Day 1: __________________________________________ Date: _________

Geometry

A ______________ indicates a location and has no size. It is represented by a ______ and is named

using a _________________ letter.

Ex:

A ____________ is represented by a straight path that extends in two opposite directions

____________ end and has no thickness. A line contains ________________ many points. A line is

named by any two points on the line or by a single lower case letter.

Ex:

A ______________ is represented by a flat _______________ that extends without end and has no

thickness. A plane contains infinitely many _____________. A plane is name by a capital letter or

by at least ____________ points in the plane that ________ ________ all lie on the same line.

Ex:

_________________ ____________: Points that lie on the same line

_________________ ____________/____________: Points and lines that lie in the same plane.

Ex 1).

a) What are two other ways to name 𝐴𝐵 ⃡ : ____________________

b) What are two ways to name plane Q? ____________________

c) What are the names of three collinear points? ________________

d) What are the names of four coplanar points? _________________

A _________________ is part of a line that consists of two ________________ and all points between

them. A segment is named by its two endpoints.

Ex:

A _________ is part of a line that consists of one ______________ and all the points of the line on one

side of the endpoint. A ray extends in ______ _________________. A ray is named by its endpoint

and another point on the ray. The ____________ of the points indicates the ray’s _________________.

Ex:

__________________ ________ are two rays that share the _________ endpoint and form a line.

Opposite rays are named by their shared endpoint and any other point on each ray.

Ex:

Ex 2).

a) What are the names of the segments in the figure? _________________________

b) What are the names of the rays in the figure? _____________________________

c) Which of the rays in part (b) are opposite rays? ________________________

Ex 3). Draw three noncollinear points R, S, and T. Then draw 𝑅𝑆 , 𝑆𝑇 ⃡ , 𝑅𝑇̅̅ ̅̅

Ex 4). Given four points:

a) Are lines 𝐴𝐵 ⃡ 𝑎𝑛𝑑 𝐴𝐶 ⃡ the same? ________

b) Are line segments 𝐴𝐶̅̅ ̅̅ 𝑎𝑛𝑑 𝐵𝐷̅̅ ̅̅ the same? _________

c) Are rays 𝐶𝐴 𝑎𝑛𝑑 𝐶𝐵 the same? ________

Homework: pg. 12 #1 – 17, 20 – 24(e)

1.2 Day 2: ___________________________________________ Date: __________

Geometry

A _________________ or ____________ is an accepted statement of fact.

Postulate 1-1: Through any ______ points there is exactly ______ _______.

Postulate 1-2: If two distinct lines intersect, then they intersect in ______________ ______ _________.

Postulate 1-3: If two distinct planes intersect, then they intersect in ______________ _______ _______.

Ex 1). Each surface represents part of a plane.

What is the intersection of plane AEH and plane EGH? _________

Ex 2). Each surface of the box represents part of a plane.

a) What is the intersectio of plane RNQ and plane JMN? _____________

b) Which plane contains points J, M, and L? ______________

c) Which plane contains points L, P, and Q? ______________

d) Which plane contains points M, J, and P? Shade below. _______________

e) Which plane contains points J, K, and Q? Shade below. ______________

f) What other point is in the same plane as points N, P, and Q? ____________

g) What other point is in the same plane as points J, M, and Q? ___________

h) What lines contain two of the four points: J, K, L, and M? _______________

_______________________________________________

j) What is the intersection of the plane JMP and plane PQL? _______________

Ex 3).

a) Name four points: _________________________________

b) Name two lines: ___________________________________

c) Name two planes: _________________________________

d) Name the intersection of the two planes: __________________

Homework: pg. 17 # 1 – 26

1.3: _________________________________________________ Date: __________

Geometry

Recap:

Postulate/Axiom is an accepted _____________

Through any two points, there is exactly one _______________

If lines intersect, they always intersect at a ________________

If planes intersect, they always intersect at a ________________

Postulate 1-5: ______________________________________

Every point on a line can be paired with a real number, called a _____________________________.

Consider, 𝐴𝐵 ⃡ at the right. The _____________________

between A and B is the absolute value of their

coordinates.

Ex:

Ex 1). Find the measure of each segment.

a). What is CD?

b). What is BD?

Postulate 1-6: ______________________________________________

If three points A, B, and C are ______________________ and B

is between A and C, then _____________________________.

Ex 2). If LN = 32, what are LM and MN?

If two segments have the same length, then the segments are _____________ (____) ______________.

Ex 3). Are 𝐴𝐷̅̅ ̅̅ 𝑎𝑛𝑑 𝐵𝐸̅̅ ̅̅ congruent?

The ________________ of a segment is a point that divides the segment into two _________________

segments. A ________, _________, _______, or other _______________ that intersects a segment at its

midpoint is said to _________________ the segment. That point, line, ray, or segment is called a

________________ ___________________.

Ex 4). S is the midpoint of 𝑅𝑇̅̅ ̅̅ . What is RS, ST, and RT?

Homework: pg. 24 #1 – 5, 8 – 24(e), 34

1.4: _____________________________________________ Date: __________

Geometry

ANGLE

Definition How to Name it Diagram

An _____________ is formed by

two ________ with the same

endpoint. The rays are the

__________ of the angle. The

endpoint is the of the angle.

You can name an angle by:

Its vertex, ___________

A point on each ray

and the vertex,

_____________________

A number, __________

The ____________ of an angle is the region containing all of the points

_______________ the two sides of the angle. The _____________ of an

angle is the region containing all of the points __________ of the angle.

Ex 1). What are three other names for ?

_________________ _________________ _________________

Postulate 1-7: _______________________________________

Consider ______ and a point A on one side of ______.

Every ray of the form ______ can be paired one to one

with a real number from _____________.

Classifying Angles

Ex 2). Find the measure of each angle and classify:

a). <LKN: _________________________________

b). <NKM: _________________________________

c). <JKN: __________________________________

Angles with the same measure are _______________ __________. This means that if ______________,

then ________________. You can also say that if ___________________, then ______________________.

Ex 3). Use the diagram, which angle is congruent to:

a). <YAD: ______________

b). <WBM: ______________

c). <ADE: ______________

Postulate 1-8: __________________________________________________

If point B is in the interior of ___________, then

_________________________________________

Ex 4). If m<ABC = 175, what are m<ABD and m<DBC?

Homework: pg. 32 #1 – 22, 28 – 30, 37 – 40

1.5: __________________________________________ Date: _________

Geometry

Types of Angles

Definition Example

______________ __________ are two

coplanar angles with a common

_____, a common ________, and no

common interior points.

_______________ ________ are two

angles whose sides are opposite rays.

______________ __________ are two

angles whose measures have a

_______ of _______. Each angle is

called the ______________ of the

other.

_______________ _________ are two

angles whose measures have a

_______ of ________. Each angle is

called the ______________ of the

other.

Ex 1). Use the diagram. Is each statement true? Explain.

a). <PAL and <LAM are adjacent angles: ___________________________

____________________________________________________________________

b). <PAO and <NAM are vertical angles: ____________________________

____________________________________________________________________

c). <PAO and <NAO are supplementary: ____________________________

There are some relationships you can assume to be true from an unmarked diagram and some

you cannot.

You CAN assume the following: You CANNOT assume the following:

1. ______________________________________ 1. ____________________________________

2. ______________________________________ 2. ____________________________________

3. ______________________________________ 3. ____________________________________

Ex 2). What can you conclude from the information in the diagram?

A _________ ________ is a pair of adjacent angles whose noncommon sides are opposite rays. The

angles of a linear pair form a _____________ __________.

Postulate 1-9: ___________________________________________________

If two angles form a ______________ _________, then they are _______________________.

Ex 3). <ABC and <DBC are a linear pair, m<ABC = 3x + 19, and m<DBC = 7x – 9. What are the

measures of <ABC and <DBC?

An __________ ____________ is a ray that divides an angle into two congruent angles.

Ex 4). 𝐿𝑀 bisects <JLN. If m<JLM = 42, what is m<JLN?

Homework: pg. 40 #1 – 28

1.6: _________________________________________________ Date: __________

Geometry

A ___________________ is a ruler with no markings on it. A ______________ is a tool used to draw

circles and part of circles called _________. A ___________________ is a geometry figure drawn

using a ___________________ and a ________________.

*See page 49 for STEPS

Ex 1). Construct 𝐸𝐹̅̅ ̅̅ so that 𝐸𝐹̅̅ ̅̅ ≅ 𝐴𝐵̅̅ ̅̅ .

Ex 2). Construct <C so that <C ≅ <A.

___________________ ___________ are lines that intersect to form right angles.

The symbol ______ means “is perpendicular to.”

A __________________ ____________ of a segment is a line, segment, or ray that is perpendicular to

the segment at its _______________.

Ex 3). Construct 𝐿𝑀 ⃡ so that 𝐿𝑀 ⃡ is the perpendicular bisector of 𝑄𝑅̅̅ ̅̅ .

Ex 4). Construct 𝐷𝐸 , the bisector of <D.

Homework: pg. 52 #1 – 4, 7 – 11

1.7 Day 1: __________________________________________ Date: __________

Geometry

Midpoint

Description Formula Diagram

On a Number Line:

The coordinate of the

midpoint is the ___________ or

_______ of the coordinates of

the endpoints.

In the Coordinate Plane

The coordinates of the

midpoint are the average of

the _______________ and the

average of the

_______________ of the

endpoints.

Ex 1). 𝑭𝑬̅̅ ̅̅ has endpoints -3 and 7. What is the coordinate of its midpoint?

Ex 2). 𝐹𝐸̅̅ ̅̅ has endpoints F(5, -10) and E(3, 6). What is the midpoint of 𝐹𝐸̅̅ ̅̅ ?

Ex 3). 𝑆𝐴̅̅̅̅ has endpoints S(-4, -2)and A(-7, 1). What is the midpoint of 𝑆𝐴̅̅̅̅ ?

Ex 4). The midpoint of 𝐿𝑀̅̅ ̅̅ is A(2, -1). One endpoint is L(-3, -5). What are the coordinates of the

other endpoint?

Ex 5). The midpoint of 𝐴𝐵̅̅ ̅̅ is T(4, -9). Endpoint A has coordinates (-3, -5). What are the coordinates

of B?

Homework: pg. 59 #1 – 3, 4 – 24(e)

1.7 Day 2: ___________________________________________ Date: __________

Geometry

Distance Formula

The distance between two points ____________ and ____________

is:

Ex 1). What is the distance between (6, -2) and (-5, 3)? Round to the nearest tenth.

Ex 2). What is the distance between (-2, 14) and (3, -1). Round to the nearest tenth.

Ex 3). On a zip-line course, you are harnessed to a cable that travels through the treetops. You

start at Platform A and zip to each of the other platforms. How far do you travel from Platform B

to Platform C?

Homework: pg. 62 #1-5, 6-18(e), 28-31

1.8 Day 1: __________________________________________ Date: __________

Geometry

The ___________________ P of a polygon is the _______ of the lengths of its sides.

Perimeter and Circumference

Square Triangle

Rectangle Circle

Ex 1). To place a fence on the outside of the garden, how much material will you need?

Ex 2). What is the circumference of the circle in terms of 𝜋? What is the circumference of each

circle to the nearest tenth?

Ex 3). What is the perimeter of triangle LMN?

Ex 4). Graph quadrilateral JKLM with vertices J(-3, -3), K(1, -3), L(1, 4) and M(-3, 1). What is the

perimeter of JKLM?

Homework: pg. 75 #1, 2, 5 – 13

1.8 Day 2: __________________________________________ Date: __________

Geometry

The _________ of a polygon is the number of square units it encloses.

Area

Square Triangle

Rectangle Circle

When measuring area, use __________ _______ such as ________, _________, _________ … Always use

the _______ unit for both dimensions.

Ex 1). You are designing a rectangular flag for your city’s museum. The flag will be 15 feet wide

and 2 yards high. How many square yards of material do you need?

Ex 2). The diameter of circle L is 10 cm. What is its area in terms of 𝜋.

Area Addition Postulate: The area of a region is the ________ of the areas of its __________________

parts.

Ex 3). What is the area of the figure below?

a)

b)

c)

Homework: pg. 75 #1, 4 – 18(e), 22