Download Pretest Review Geometry

Reviewing skills needed to succeed in
Geometry.
• Cross Product Property!!
a c

b d
Example:
3
2

x 5 3
ad = bc
Answer :
3(3)  2( x  5)
9  2 x  10
19  2 x
19
x
2
• Has 4 quadrants
• The origin is at (0,0)
• Coordinates are (x, y). X is horizontal coordinate, y is vertical
coordinate
•
•
•
•
•
Parallel lines = same slope
Perpendicular lines = opposite, reciprocal slope
Vertical lines = undefined slope (Equation is x = a )
Horizontal lines = slope of 0 ( Equation is y = b)
To find the slope between 2 points on a line:
y2  y1
m
x2  x1
• Slope Intercept: y = mx + b
m= slope, b = y intercept
(we will use this most often in this class)
• Standard Form: Ax + By = C
• Point Slope Form: y – y1 = m (x – x1)
m = slope, (x1, y1) = any point on the line
• Need a point on the line and the slope of the line
• If given 2 points, find the slope first, then use either point
• Use algebra to move back and forth between forms of a line
Example: Write the equation in slope intercept form of the line
that passes through point (-2, 1) and has a slope of 3.
Answer :
y  mx  b
1  (3)(2)  b
1  6  b
b7
Equation : y  3 x  7
•
•
•
•
X – intercept : y coordinate= 0
Y- intercept : x coordinate = 0
Can graph using intercepts or in slope-intercept form
To graph in slope-intercept: graph the y-intercept, use slope to
graph other points
• Graph the equation: y=2x+1
y intercept: 1
Slope: 2
#20 on packet:
• Since y is isolated in equation 1, we can use the substitution
method.
• Substitute 3x-5 from the first equation in for y in the second.
Answer :
• Then solve for x.
y  3x  5
• Use this value to find y.
4 x  3 y  35
4 x  3(3 x  5)  35
4 x  9 x  15  35
 5 x  15  35
 5 x  50
x  10
y  3(10)  5  25
Answer  (10,25)
• Perimeter: The sum of the lengths of the sides of a polygon
(called circumference for circles)
• Units of measurement: in, yds, ft, miles, meters, etc..
• Area: The number of square units a polygon encloses
• Units of measurement: in2, cm2, mi2, etc…
•
Volume: How much space an object takes up
• Units of measurement: in3, cm3, mi3, etc…
Answer :
Volume  l  w  h
 12(6)(5)
 360un 2
SurfaceArea  2lw  2 wh  2lh
 2(12)(6)  2(6)(5)  2(12)(5)
 144  60  120
 324un 2
1
Area = bh
2
h
b
• Radius: r
• Diameter: d =2r
• Circumference:
•
C= d OR
•
C= 2 r
• Area: A =  r2
r
d
• If directions say leave in terms of  , THEN LEAVE THE  IN
YOUR ANSWER!!!! Otherwise, use  button on calculator.
Line:
A series of points that extends in 2 opposite directions
without end
Can name a line by any two points on the line with a
line above it, or by a single lower case letter.
(Please note: In Geometry, it is important to use the
correct notations!!)
1. Name a line.
Examples :
AB, EF , CB, etc.
• A flat surface that has no thickness
• Contains many lines
• Extends w/o end in the direction of all its
lines
• Named by a single capital letter OR by
AT LEAST 3 POINTS NOT ON THE SAME
LINE
Parallel Lines: lines that do not intersect that are on the same
plane
(to name parallel lines, you can use the symbol ||)
1. Name 2 parallel
segments.
AD || BC
C
D
B
A
Planes that do not intersect
F
E
C
D
Example:
1. Name a plane parallel
to plane EGA.
Answer: Plane FCB
H
G
A
B
• Segment: part of the line consisting of 2 endpoints and all
the points between them
• How you name a segment: Use the 2 endpoints with a
straight line above.
• Ray: part of a line consisting of one endpoint and all the
points of the line on one side of the endpoint
• How you name a ray: Endpoint must be first, then any other
point on the ray; write an arrow pointing to the right above
1.
A
B
2.
A
B
AB
or
AB
or
BA
AC
Read “segment AB” or “segment BA”
Read “Ray AB” or “Ray AC”. DO
NOT write Ray BA or Ray CA.
Must name endpoint first!!
C
• Classify by sides: Scalene, Isosceles, or Equilateral
• Classify by angles: Acute, Obtuse, Straight or Right
• All angles add up to 180˚
• All straight angles form a line, therefore measure 180˚
• Supplementary: 2 angles that add up to 180˚
• Complementary 2 angles that add up to 90˚
ANGLE (  ): Formed by 2 rays with the same endpoint
1
To name an angle:
3 possible ways:
E
1
FED, DEF
Notice vertex is middle letter!
To indicate angle measure:
mE 
(angle measure in degrees)
1
2
• Must name using a numbered angle or using 3
points with vertex in the middle.
• Cannot write “ angle B”.
1  CBA
2  DBA
 MUST be used on a right triangle
 c is the hypotenuse, a and b are the legs of the right triangle
2
a
+
2
b
=
2
c
ALTERNATE INTERIOR ANGLES:
• Non-adjacent
• Lie on opposite sides of the transversal in between the
2 lines it intersects
C , B
and
A, D
• Lie on the same side of the transversal between the two lines
• Lie outside the 2 lines on opposite sides of the transversal
• Lie outside the 2 lines on same side of
transversal
1, 8
and
2, 7
• Lie on the same side of the transversal
• In corresponding positions
o, s
or
p, t
or
n, r
or
m, q
12 3  4 4


15 3  5 5
Look for common factors, and cancel them out to 1.