Download Name: Geometry (A) Unit 1: Supplemental Packet Supplements 1

Name:
Geometry (A)
Unit 1: Supplemental Packet
Supplements
1-1 : Nets and Drawings for Visualizing Geometry
A net is a two-dimensional diagram that you can fold to form a three-dimensional figure.
A net shows a three-dimensional figure as a folded-out flat surface.
1. If the net at the right folds into the cube beside it, which letters
will be on the top and front of the cube?
Top _______
Front _______
2. If the net in problem 1 folds into the cube at the right, which
letters will be on the top and right side of the cube.
Top _______
Right _______
3. What is the net for the graham cracker box to the right?
Label the net with its dimensions.
4. What is the net for the figure at the right?
Label the net with its dimensions.
 Think: How many surfaces (shapes) does the figure contain?
Do all the rectangles have the same dimensions?
Is there only one possible net drawing for the figure at the right? If not, draw another.
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5. What is the net for the figure on the right? Label the net with its dimensions.
An isometric drawing shows a corner view of a three-dimensional figure. It allows you to
see the top, front, and side of the figure.
An orthographic drawing is another way to represent a three-dimensional figure. An
orthographic drawing shows three separate views: a top view, a front view and a right-side
view.
Can you visualize the orthographic drawing
for the isometric drawing at the right? Try to draw it.
Top view:
Front view:
Right-side view:
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How close were you?
Additional Practice:
1. The net below folds into a cube. Which letters will be
on the top and front of the cube?
Top _______
Front _______
2. What is the net for the cereal box at the right?
Label the net with its dimensions.
3. What is the front orthographic drawing
for the isometric drawing below?
HW 1-1: Practice 1-1 WS
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Supplements
1-2: Points, Lines, and Planes
1-3: Measuring Segments
Important Postulates and Theorems
To Remember!
Use the diagram below to answer the following.
Give two other names for line PQ:
Give two other names plane R:
Name three points that are collinear:
Name four points that are coplanar:
Give two other names for line ST:
Name a point that is not coplanar with points Q, S,
and T:
Draw a sketch of the given question then solve.
1. Line RS bisects PQ at point R. Find RQ if PQ = 14 cm.
2. Point T is a midpoint of UV. Find UV if UT = 4 ½ yards.
In the diagram, M is the midpoint of the segment. Find the indicated length.
3. Find LN
4. Find MR
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Supplements
1-4: Measuring Angles
1-5: Exploring Angle Pairs
Important Postulates and Theorems To Remember!
VERTICAL ANGLES ARE CONGRUENT
1. DEF is a straight angle. What is the mDEC
and mCEF?
2. Are BFD and CFD adjacent angles? Explain.
3. Are AFB and EFD are vertical angles? Explain.
Additional Examples
1) Name the three angles in the diagram. Why can’t you just call this angle B???????
_______ , or _______
_______ , or _______
_______ , or _______
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2) Name the three angles in the diagram. Why can’t you just call this angle G???????
_______ , or _______
_______ , or _______
_______ , or _______
3) What type of angles do the x and y axis form in the coordinate plane? _________________
4) Given that m  GFJ = 155o, find
a) m  GFH __________
b) m  HFJ __________
5) Given that  VRS is a right angle, find
a) m  VRT __________
b) m  TRS __________
6) Identify all pairs of congruent angles in the diagram. If m  P = 120o, what is m  N?
 _______   _______
 _______   _______
m  N = ______o
7) WY bisects  XWZ, and m  XWY = 29o.
Find m  XWZ _________o
8) Identify all pairs of congruent angles in the diagram. If m  B = 135o, what is m  A?
 _______   _______
 _______   _______
m  A = ______o
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9) KM bisects  LKN and m  LKM = 78o.
Find m  LKN _________o
10) Two angles form a linear pair. The measure of one angle is 4 times the measure of the
other. Find the measure of each angle.
11) The exterior sides of two adjacent angles are opposite rays. The measure of one angle
is 3 times the measure of the other. Find the measure of each angle.
12) In the diagram:
a) All points shown are _________________.
b) Points A, B, and C are ________________.
c)  DBE and  EBC are ______________ angles.
d)  ABC is a ____________ angle.
13) Find m<EGT and m<TGC if EG is perpendicular to CG, and m<EGT = 7x + 2 and
m<TGC = 4x.
14) Find the value of each angle.
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Supplements
1-7: Midpoint and Distance in the Coordinate Plane
Find the coordinates of the midpoint of the segment with the given endpoints.
1. L(4, 2) and P(0, 2)
2. G(-2, -8) and H( -3, -12)
Using the given point R and the midpoint M, find the other endpoint.
3. R(6, 0), M(0, 2)
4. R( 3, 4), M(3, -2)
Horizontal & Vertical Lines
Find the length of line segment GF: _________
Find the length of line segment HJ: _________
So, GF _____ HJ
Find the length of the line segment. Round to the nearest tenth of a unit. If there are
two segments compare the lengths.
5.
6. RS: R(5, 4), S(0, 4)
TU: T(-4, -3), U(-1, 1)
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7. Suppose point P partitions the directed line segment from L to M in the
ratio 2 to 1. You can think of LM as being divided into 3
congruent parts so that the length of LP is 2 parts and the length
of PM is 1 part.
The directed line segment from L to M starts at L and ends at M.
1) Graph L at (-4,1) and M at (5,-5)
2) As you move from L to M, the horizontal distance is __________ (right/left) and the
vertical distance is ______(up/down).
3) Divide each of these distances by 3: horizontal / 3 = _______
4) Multiply each of these distances by 2: horizontal * 2 = _______
vertical / 3 =________
vertical * 2 = _______
5) Move L(-4, 1) _____ to the(right/left) and _______ (up/down) … where does the point
P go? (
,
).
REASONING
How did you know where to start? _________________________________________________________________
Why did you divide the segment into 3 parts? ____________________________________________________
Why do you make this move 2 times? _____________________________________________________________
How did you know where to put P? ________________________________________________________________
8. RS is the directed line segment from R(-2,-3) to S(8,2). What are the coordinates of
point Q that partitions the segment in the ratio 2 to 3?
The directed line segment from R to S starts at ______ and ends at ______.
1) Graph R at (-2,-3) and S at (8, 2) Optional – On Your Own Graph Paper!
2) As you move from R to S, the horizontal distance is __________ (right/left) and the
vertical distance is ______(up/down).
3) Divide each of these distances by 5:
horizontal / 5 = _______
vertical / 5 =________
4) Multiply each of these distances by 2: horizontal * 2 = _______
vertical * 2 = _______
5) Move R(-2, -3) _____ to the(right/left) and _______ (up/down) … where does the point
Q go? (
,
).
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9. Point C lies on the directed line segment from A(5, 16) to B(-1,2) and partitions the
segment into a ratio of 1 to 2. What are the coordinates of C?
The directed line segment from A to B starts at ______ and ends at ______.
1) Graph A at (5,16) and B at (-1,2) Optional – On Your Own Graph Paper!
2) As you move from A to B, the horizontal distance is __________(right/left) and the
vertical distance is ______(up/down).
3) Divide each of these distances by 3:
horizontal / 3 = _______
4) Multiply each of these distances by 1: horizontal * 1 = _______
vertical / 3 =________
vertical * 1 = _______
5) Move A(5, 16) _____ to the(right/left) and _______ (up/down) … where does the point
C go? (
,
).
10. The endpoints of directed line segment XY are X(2,-6) and Y(-6,2). What are the
coordinates of point P on XY such that XP is ¾ of the distance from X to Y?
The directed line segment from X to Y starts at ______ and ends at ______.
1) Graph X at (2,-6) and Y at (-6, 2) Optional – On Your Own Graph Paper!
2) As you move from X to Y, the horizontal distance is __________ (right/left) and the
vertical distance is ______ (up/down).
3) Multiply each of these distances by 3/4: horizontal * 3/4 = _______
vertical * 3/4 = _______
4) Move X (2, -6) _____ to the(right/left) and _______ (up/down) … where does the point
P go? (
,
).
Optional Formula to partition any line segment with endpoints (x1, y1) , (x2, y2) into a
ratio of m:n: ( (mx2 + nx1)/(m+n) , (my2 + ny1)/(m+n) )
Try this on the problem #9 above:
m = ________
n = ________
x1 = ________
x2 = ________
y1 = ________
y2= ________
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Supplements
1-8: Perimeter, Circumference and Area (With Review of Polygons)
Classifying Polygons
Polygon
_________________________________________________________________________________________________________
_________________________________________________________________________________________________________
_________________________________________________________________________________________________________
Convex Polygon
_________________________________________________________________________________________________
Concave Polygon
_________________________________________________________________________________________________
n-gon _________________________________________________________________________________________________
Equilateral Polygon ________________________________________________________________________________
Equiangular Polygon _______________________________________________________________________________
Regular Polygon______________________________________________________________________________________
Names of Polygons
Name
Sides
Name
Sides
3
11
4
12
5
n
6
7
8
9
10
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1. Tell whether the figure is a polygon and whether it is convex or concave.
a)
b)
c)
2. The head of a bolt is shaped like a regular hexagon. The expressions shown
represent side lengths of the hexagonal bolt. Find the length of a side.
3. The expressions (4x + 8)o and (5x – 5)o represent the measures of two congruent
angles . Find the measure of an angle.
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1. Find the dimensions of the garden,
including the path.
2. What is the circumference and area of the
circle in terms of ? What is the
circumference and area of the circle to the
nearest tenth?
3. What is the area and perimeter of EFG?
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?
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5. You are designing a poster that will be 3 yds wide and 8 ft high. How much paper do you
need to make the poster? Leave your answer in terms of feet.
6. What is the area of the figure at the right? All angles are right angles.
7. Triangle JKL has vertices J(1, 6), K(6, 6) and L(3, 2). Find the approximate perimeter and
area of triangle JKL. Round all answers to the nearest tenth.
8. The base of a triangle is 24 feet. Its area is 216 square feet. Find the height of the
triangle.
HW 1-8: Practice 1-8 WS
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