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Name _____________________
Algebra & Geometry Review
Geometry
Topic 1
Language of
Geometry
PROBLEM PACKET
Algebra & Geometry Review
Geometry Topic 1 Problem Packet
1
Homework Assignments!!
Assignment
Number
Description of Assignment
Algebra & Geometry Review
Date
Assigned
Geometry Topic 1 Problem Packet
Date
Due
2
1.1 Mathematical Word Roots
The definitions of many words in geometry are directly related to their word roots.
1. Pentagon –
Word Root 1: PENTA meaning five, Word Root 2: GONIA meaning angle
Definition of Pentagon: a five sided figure (has five angles too)
2. Concentric –
Word Root 1: CON meaning with or same, Word Root 2: CENTRE meaning center
Definition of Concentric : Concentric circles have the same center
Directions: Complete the table by finding the one or two Latin/Greek roots, their meaning, and
the definition of each geometry term in the table. Use your notes!
Geometry Term
Root
1
Meaning
Root
2
Meaning
Definition of Geometry Term
Polygon
Trisect
Quadrilateral
Triangle
Isosceles
Circumference
Hemisphere
Intersect
Rectangle
Bisect
Collinear
Sesquicentennial*
Democracy*
Calorie*
*These words aren’t directly related to geometry. See if you can break them down into their
roots. Use the Internet if you need help.
Algebra & Geometry Review
Geometry Topic 1 Problem Packet
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1.2 Points, Lines, and Planes
Geometry is based on the fact that points, lines, and planes have no definitions.
It is upon these words that the basic structures of geometry are built. Each of these
structures has a unique way in which we write them. Consider the following example:
Some examples from the diagram
to the right:
1. 3 points: J, A, and K
sur
2. A line containing H and I: HI
3. A plane: plane GHI
4. A segment with K and G as
endpoints: KG
5. A ray starting at A and passing
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through J: AJ
Directions: For #1 – 6, write each of the following using the appropriate symbols:
1. The segment with endpoints T and S
2. The ray that begins at R and passes through P
3.
4.
5.
6.
7. Draw a line that passes through A, B, and C. Name it using appropriate symbols.
8. Draw a line segment and name it two different ways.
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Geometry Topic 1 Problem Packet
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1.2 Points, Lines, and Planes (cont.)
Directions: For #9 – 12, sketch the following:
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9. Draw ST
10. Draw AB
11. Draw J
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12. Draw NB
Directions: For #13 – 22 refer to the picture to the right.
13.
14.
15.
16.
17.
18.
19.
20.
Name four points.
Name three lines.
Name three rays.
Name two segments that contain I.
Name two lines that contain J.
Name a plane.
Name the point that is between J and I.
Name the point that is common to three
lines.
21. Name three non-collinear points.
22. Name three collinear points.
23. Use the idea of a line segment to describe a triangle.
24. Use the idea of a line segment to describe a six-sided figure.
suur suur
suur
25. Draw a figure with points B, C, D, E, F, and G that shows lines CD , BG , and EF , with C
on all three lines.
Directions: For #26 – 28, how many different lines can you create that contain at least 2 points?
26.
27.
28.
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Geometry Topic 1 Problem Packet
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1.3 Naming Angles
Angles have different parts and we name them in a certain way:
The sides of an angle are the two
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rays that intersect: DG and DM
are the sides of this angle
The vertex of an angle is the
point where the two sides meet:
D is the vertex of this angle
You name an angle using
three points where the
vertex of the angle must
go in the middle: This
angle is called ÐGDM or
ÐMDG .
Sometimes angles are
numbered and it’s OK to
use that number. We can
also call this angle Ð1.
Part I: Place a word from the list below in each of the blank spaces in the paragraph.
(Each word is used only once.)
Vertex
Sides
Three
Rays
Vertex
Angle
Vertex
An _______________________ is formed when two rays meet at their endpoints. The two
_________________ that intersect to form an angle are called the _________________ of the
angle. The endpoint where the two rays intersect is called the ______________________ of the
angle. An angle is named using ____________________ points: one point on one of its sides,
then the ______________________, and a point on the other side. The ____________________
is always the second point used to name the angle.
Part 2: Draw the following angles:
1. ÐTVE
2. ÐTEV
3. ÐETV
4. For the angle in question 3, how many different ways could you correctly name it?
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Geometry Topic 1 Problem Packet
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1.3 Naming Angles (cont.)
Part III. Name the numbered angles in each drawing.
5.
6.
7.
8.
9.
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Geometry Topic 1 Problem Packet
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1.4 Midpoints and Bisectors
A midpoint is a point that cuts a line segment into two congruent parts.
A bisector is a more general term for a ray, line, or line segment that divides something
else into 2 congruent parts.
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Ex: Suppose AB bisects
Ex: Suppose M is the midpoint
ÐCAD . If mÐCAD = 60o ,
then, mÐCAB = mÐBAD = 30o
of AB . If AB = 6 cm, then
AM = MB = 3cm
1. Explain what a midpoint is. Draw a diagram that contains a midpoint and mark it
appropriately to show that the point you drew is actually a midpoint.
2. Explain what a segment bisector is.
3. Explain what an angle bisector is.
Directions: For #4 – 7, sketch the following pictures and be sure to mark them appropriately.
4. AB bisects CD
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5. HK bisects ÐPHR
6. M is the midpoint of TV
suur
7. GH bisects BX at H
Directions: For #8 – 14, answer the following questions based on this diagram.
8. Name a ray
9. Name a line
10. Name a segment
11. Name the segment bisector
12. Name a midpoint
13. Name a point that is not a
midpoint
14. Name an angle
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Geometry Topic 1 Problem Packet
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1.4 Midpoints and Bisectors (cont.)
Directions: For #15 – 18, answer the following questions based on this diagram.
15.
16.
17.
18.
Name the angle bisector
Name the angle that is being bisected
What is mÐTPK ?
What is P called?
We sometimes want to describe points that are not necessarily midpoints.
The segment addition postulate says that if C is a point on AB , then AC + CB = AB
Ex: Since AC+ CB = AB, we know that
AB = 7 cm.
19. If C is a point on AB and AC = 3 in and CB = 1.5 cm, find AB.
20. If C is a point on AB and AB = 12 mm, and AC = 8 mm, find CB.
21. If E is a point on DF and DE = x + 2, EF = 8, and DF = 15, find the value of x.
22. If E is a point on DF and DE = 3x and, EF = 6, and DF = 24, find DE.
Algebra & Geometry Review
Geometry Topic 1 Problem Packet
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Algebra & Geometry Review
Geometry Topic 1 Problem Packet
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