Download Introduction to Geometry Review

Geometry 1:
Introduction to Geometry Review
Name ______________________________________
Period _______________ Date _________________
G-CO.1: Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line.
1.
3. In the figure SP bisects RST ,
mRSP  (9 x  14) , and mTSP  ( x  74) . Solve
for x and find mRST
Use the figure
at the right.
Assume that
lines that look
parallel are
parallel and
lines that look
perpendicular
are
perpendicular.
a) Name a pair of parallel segments
b) Name a pair of perpendicular segments
4. Given the following, find the length of TL and TO .
c) Name a pair of skew segments
2. Use the diagram
at the right to
answer the
following
questions.
a) Name a linear
pair
b) Name two complementary angles
- T is the midpoint of XO
- The length of XO is 10
- HL is 8
c) Name two supplementary angles
d) Name two adjacent angles to ∠ORN
e) Name a pair of vertical angles
TL = ____________
TO = ____________
Geometry: Intro to Geometry Review
PUHSD Curriculum Team
5. Using the diagram below, find x and justify each
step.
AEB  BEC .
Solve:
Part A: Draw a diagram that satisfies these three
conditions
(4x)°
x°
Steps:
7. You know that AEB  CED ,
BEC is adjacent to CED , and
20°
Justification:
Part B: If 𝑚∠𝐴𝐸𝐵 = 30°, find
𝑚∠𝐵𝐸𝐶, 𝑚∠𝐶𝐸𝐷 𝑎𝑛𝑑 𝑚∠𝐴𝐸𝐷. Justify your
answers.
_________________________________
__________________________________
__________________________________
6. Circle all of the following statements that are
definitely true about the diagram below.
(There may be more than one answer.)
__________________________________
G-CO.12: Make formal geometric constructions with a
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a
line segment; and constructing a line parallel to a given line
through a point not on the line.
8. Construct the perpendicular bisector of RP
R
(a) AEB  DEC
(b) AEC is adjacent to BED
(c) AEB and BEC are complementary
(d) DEC and BEC are complementary
(e) EC bisects BED
(f) DEA is supplementary
Geometry 1: Intro to Geometry Review
P
PUHSD Geometry Curriculum Team
9. Given  A construct its bisector.
11. Given the diagram below,
Name a pair of each of the following.
Alternate interior angles _________________
G-CO.9: Prove theorems about lines and angles. Theorems
include: vertical angles are congruent; when a transversal
crosses parallel lines, alternate interior angles are congruent
and corresponding angles are congruent; points on a
perpendicular bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
Same side interior angles ________________
Vertical angles ________________________
Alternate exterior angles ________________
Corresponding angles __________________
10. Given that lines a line b.
Linear Pair __________________________
12. Which lines, if any, must be parallel based on the
given diagram and information. Justify your answer.
Given: 13  12
a
1
2
9 10
3 4
Part A: Find the value of x.
b
11 12
5
6
7
8
c
Part B: Describe the relationship between these two
angles.
13 14
15 16
d
_____________________________________________
_____________________________________________
_____________________________________________
Geometry 1: Intro to Geometry Review
PUHSD Geometry Curriculum Team
G-GPE.4: Use coordinates to prove simple geometric
G-GPE.5: Prove the slope criteria for parallel and
theorems algebraically. For example, prove or disprove that a
figure defined by four given points in the coordinate plane is a
rectangle; prove or disprove that the point (1, √3) lies on the
circle centered at the origin and containing the point (0, 2).
perpendicular lines and use them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a
given line that passes through a given point).
15. Given the equation y = - 4x + 8
13. Given X(-2, 3) and Y(3,-1).
Part A: Find the midpoint.
Part A: Give an example of a line parallel to the one
given above.
Part B: Find the distance.
Part B: Give an example of a line perpendicular to the
one given above.
Part C: Find the slope.
16. Given the equation 6y - 2x = 18.
14. Given the following coordinates A (-1,6) and
B (3,-2). Find the midpoint of AB and label it M. How
would you prove that M is the midpoint?
y
Part A: What is the slope of this line?
Part B: Write an example of an equation of a line that
is perpendicular to the original line.
10
Part C: Write an example of an equation of line that is
parallel to the original line.
–10
10
x
–10
Geometry 1: Intro to Geometry Review
PUHSD Geometry Curriculum Team