Download Geometry 1 - Phoenix Union High School District

Geometry 1: Intro to Geometry
Introduction to Geometry
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.
3. In the figure MO bisects LMN ,
mLMO  (9 x  14) , and mNMO  ( x  74) .
Solve for x and find mLMN
1. Use the figure below. Assume that lines that look
parallel are parallel.
a) Name a pair of
parallel lines
b) Name a pair of perpendicular lines
4. In the figure ST bisects UX , If UW  8 x  4 ,
and WX  2 x  20 . Solve for x and find UX
2. Use the diagram below to answer the following
questions.
S
W
U
B
C
A
X
T
D
O
E
5. If x
100, then what are the possible values of y?
2a) Name a linear pair
x°
y°
2b) Name two complementary angles
2c) Name two supplementary angles
2d) Give at least two pairs of adjacent angles
Geometry: Intro to Geometry Review
(May 30, 2014)
PUHSD Curriculum Team
6. If x < 35, then what are the possible values of y?
9. Part A: Draw a diagram that satisfies these three
conditions:
i. AEB  CED
ii. BEC is adjacent to CED
iii. AEB  BEC
y°
x°
7. Using the diagram below, find x and explain how
you would tell a fellow student to solve it.
Part B: If
, find
. Justify your
answers.
Solve:
_________________________________
__________________________________
(4x)°
x°
20°
__________________________________
__________________________________
Explain___________________________
__________________________________
__________________________________
8. Write down as many facts as are observable from
the figure below. (Need at least 3)
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.
10. Construct the perpendicular bisector of RP
R
P
Geometry 1: Intro to Geometry Review
(May 29, 2014)
PUHSD Geometry Curriculum Team
11. Draw acute angle ABC and then construct its
bisector. Label all your points.
12. Draw a right angle and then construct its bisector.
Label all your points. What are the measures of the
two smaller angles?
13. Construct a copy of the angle.
14. Use a straightedge and compass to construct a
segment that satisfies SN = 2(SU) and that all of the
points are collinear. Explain why U is the midpoint of
SN?
S
U
Explain:
_________________________________
__________________________________
__________________________________
__________________________________
Geometry 1: Intro to Geometry Review
(May 29, 2014)
PUHSD Geometry Curriculum Team
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.
15. Draw a diagram that fits the following criteria:
Draw two lines and a transversal such that  1 and
 2 are corresponding angles,  2 and  3 are
vertical angles, and  3 and  4 are corresponding
angles. What type of angle pair is  1 and  4?
G-GPE.4: Use coordinates to prove simple geometric
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).
17. Given the following coordinates A (-1,6) and
B (3,-2). Find the midpoint and length of AB.
16. Which lines, if any, must be parallel based on the
given diagram and information. Give the justification for
each conclusion. Given: 13  12
a
1
2
G-GPE.5: Prove the slope criteria for parallel and
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).
9 10
3 4
11 12
18. Given the equation 6y - 2x = 18, what would the
slope of the line be that is:
b
5
6
7
8
c
13 14
15 16
a) Perpendicular
d
b) Parallel
Geometry 1: Intro to Geometry Review
(May 29, 2014)
PUHSD Geometry Curriculum Team