Geometry
review
by Ms. Jennifer Heins
Line:

continues in both directions forever
X
Y
XY, XZ, YZ
Z
line segment

part of a line that has two endpoints
B
A
AB, BA
ray

part of a line that has one endpoint
R
T
V
RT, RV
angle

figure formed by two rays that have the
same endpoint (the vertex)
W
vertex
X
Z
WXZ
ZXW
X
Copy a line segment
Q
P
measure
X
Y
measure
mark
Copy an angle
A
Z
Y
X
B
C
bisect an angle
C
J
P
H
construct a parallel line
P
measure
X
Z
measure
Y
Construct a perpendicular bisector
A
B
construct a perpendicular line - through a point
P
Translation (slide)

To translate a figure a units to the right


To translate a figure a units to the left


decrease the x-coordinate of each point a
units
To translate a figure a units up


increase the x-coordinate of each point a
units
increase the y-coordinate of each point a
units
To translate a figure a units down

decrease the y-coordinate of each point a
units
Reflections (flip)

The reflection of point (a,b) across the x-axis is
(a, -b)

The reflection of point (a, b) across the y-axis
(-a, b)
Rotation (turn)

The rotation of the point (a, b) 90°
clockwise about the origin
(b, -a)

The rotation of the point (a, b) 180° about
the origin
(-a, -b)
congruent figures
same size
 same shape
 (cookie cutter figures)

similar figures
same shape
 corresponding angles are congruent
 ratios of their side lengths are equal
 symbol: ~

ABC ~ XYZ
C
Z
Y
A
B
X
Dilation

To dilate a figure with respect to the
multiply
origin, _________
the coordinates of each
of its points by the dilation.

larger
dilation > 1 = _____________

dilation < 1 = _____________
smaller

same size
dilation = 1 = _____________
Scale Factor of Dilations
Perimeter scale factor =
scale factor of the figures
Area scale factor =
square of the scale factor of the figures
Cross-sections of a cube
Cross-sections of a cube (cont.)
for more on cross sections of cubes, go to
www.nlvm.usu.edu/en/nav/vlibrary.html
Cross sections of Rectangular Prisms
Cross Sections of Cones
Cross Sections of Cylinders
Cross Sections of Pyramids
horizontal cross section of a
pyramid is always the shape of
the pyramid’s base
Cross Sections of Pyramids (cont.)
vertical cross section of a
pyramid is always a triangle
Cross Sections of Spheres
Always a circle
forming 3-d figures
forming 3-d figures (cont.)
forming 3-d figures (cont.)
forming 3-d figures (cont.)
forming 3-d figures (cont.)
forming 3-d figures (cont.)