Download 1.1: Date: ______ Geometry A ______ is a two

1.1: _________________________________________________
Geometry
Date: __________
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: __________________________________________
Geometry
Date: _________
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? ________________________
⃡ , 𝑅𝑇
̅̅̅̅
Ex 3). Draw three noncollinear points R, S, and T. Then draw 𝑅𝑆, 𝑆𝑇
Ex 4). Given four points:
a) Are lines ⃡𝐴𝐵 𝑎𝑛𝑑 ⃡𝐴𝐶 the same? ________
b) Are line segments ̅̅̅̅
𝐴𝐶 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐷 the same? _________
c) Are rays 𝐶𝐴 𝑎𝑛𝑑 𝐶𝐵 the same? ________
Homework: pg. 12 #1 – 17, 20 – 24(e)
1.2 Day 2: ___________________________________________
Geometry
Date: __________
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: _________________________________________________
Geometry
Date: __________
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 _____________________________.
⃡ at the right. The _____________________
Consider, 𝐴𝐵
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 ̅̅̅̅
𝐴𝐷 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐸 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
________________ ___________________.
̅̅̅̅. What is RS, ST, and RT?
Ex 4). S is the midpoint of 𝑅𝑇
Homework: pg. 24 #1 – 5, 8 – 24(e), 34
1.4: _____________________________________________
Geometry
Definition
An _____________ is formed by
two ________ with the same
endpoint. The rays are the
__________ of the angle. The
endpoint is the of the angle.
Date: __________
ANGLE
How to Name it
Diagram
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: __________________________________________
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: ____________________________
Date: _________
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: _________________________________________________
Geometry
Date: __________
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 ̅̅̅̅
𝐸𝐹 so that ̅̅̅̅
𝐸𝐹 ≅ ̅̅̅̅
𝐴𝐵.
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 ̅̅̅̅
𝑄𝑅.
Ex 4). Construct 𝐷𝐸, the bisector of <D.
Homework: pg. 52 #1 – 4, 7 – 11
1.7 Day 1: __________________________________________
Geometry
Date: __________
Midpoint
Description
On a Number Line:
Formula
Diagram
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). ̅̅̅̅
𝑭𝑬 has endpoints -3 and 7. What is the coordinate of its midpoint?
Ex 2). ̅̅̅̅
𝐹𝐸 has endpoints F(5, -10) and E(3, 6). What is the midpoint of ̅̅̅̅
𝐹𝐸 ?
Ex 3). ̅̅̅̅
𝑆𝐴 has endpoints S(-4, -2)and A(-7, 1). What is the midpoint of ̅̅̅̅
𝑆𝐴?
̅̅̅̅ is A(2, -1). One endpoint is L(-3, -5). What are the coordinates of the
Ex 4). The midpoint of 𝐿𝑀
other endpoint?
̅̅̅̅ is T(4, -9). Endpoint A has coordinates (-3, -5). What are the coordinates
Ex 5). The midpoint of 𝐴𝐵
of B?
Homework: pg. 59 #1 – 3, 4 – 24(e)
1.7 Day 2: ___________________________________________
Geometry
Date: __________
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: __________________________________________
Geometry
Date: __________
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: __________________________________________
Geometry
Date: __________
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