SAT Prep
A.) Terminology and Notation
Lines / Rays / Segments
AB, AB, AB
Angles – Classification
Straight - 180°
Vertical - =
Circle – 360°
Ex. In the figure below R, S, and T are all on line l. What is
the average of a, b, c, d, and e?
180
b c d

 36
a
5
e
l
R
S
T
Ex. In the figure, what is the value of a?
3a
c
b
(a+2b)
3a  a  2b
bc
3a  b  180
b  180  3a
3a  a  2 180  3a 
3a  360  5a
8a  360
a  45
Ex. In the figure, what is the value of x?
3 x  10  5  x  2
(3x+10)
5(x - 2)
3x 10  5 x 10
2 x  20
x  10
Ex. Line m bisects AOB, what is the value of x?
A
O
x
l
AOC  180 130  50
m
130
B
k
50
x
 25
2
B.) Parallel Lines – 4 pair of congruent angles. – Know
angle theorems.
Perpendicular to Parallels Thm.
Ex. In the figure below l // m, find the value of x.
k
m
x
140
40
l
by Alternate Interior Angles Thm.
x  40
Ex. Given AB // CD in the figure below, find the value of
x.
A
B
 x  90  37  53
37
x
C
D
37 by Alternate Interior Angles Thm.
Ex. Given the figure below l // m, find the value of a + b.
a
m
a  b  45
a
45
b
b
l
IN GENERAL – Sum of angles of all polygons = (n-2)180
Sum of the exterior angles = 360 degrees
A.) Classification
by angles : Acute
Right
Obtuse
by sides:
Isosceles
Equilateral
Scalene
Ex. Given the figure below, find x.
25
x
35
x  90  25  65
120
Ex. Given the figure below, find a.
a  75  45  120
75
45
a
B.) Theorems
1.) Exterior Angle Thm.
2.) Largest Side is opposite Largest Angle.
3.) Smallest side GREATER THAN the DIFF. of other
two.
4.) Largest side LESS THAN the SUM of the other two.
5.) PYTHAGOREAN THEOREM – a 2  b 2  c 2
Know Triples Esp. 3 – 4 – 5 and multiples
C.) Special Right Triangles –
45º – 45º – 90º
s 2
45
s
45
s
30º – 60º – 90º
2x
30
x 3
60
x
Ex. What is the area of a square whose diagonal is 10?
10
5 2
2
10

A 5 2

2
 50
Ex. In the diagram, if BC = 6 , what is the value of CD?
D
4
2 2
2
B
2 2
45
30
6
C
Ex. If the lengths of two sides of a triangle are 6 and 7, what
are the possible values of the third side?
76  x  76
1  x  13
D.) AREA of a TRIANGLE
1.) ½ bh
1
2.) ab sin C
2
3.) Equilateral =
s2 3
4
Ex. Find the area of an equilateral triangle whose side is 10.
s2 3
A
4
10 

A
2
4
A  25 3
3
Ex. An equilateral triangle with an area of 12 3 has what
perimeter?
s2 3
A
4
s2 3
12 3 
4
48  s 2
48  s
4 3s


P  3 4 3  12 3
Ex. A triangular traffic island with a flat surface is formed by
the intersection of three streets. Two of the sides of the islands
have lengths of 6.4 meters and 10.8 meters. If the measure of
the angle between these two sides is 55º, what is the area, in
square meters, of the triangular surface of the island?
55
6.4
10.8
h
h
sin 55 
6.4
h  6.4sin55  5.24
1
A  10.8  5.243  28.3
2
OR
1
A  ab sin C
2
1
A  10.8  6.4  sin 55  28.3
2
E.) SIMILAR TRIANGLES
3 pairs of = angles
3 pair of proportional sides
Ex. Given the figure below, find BC.
4
A
4
D
3
B
AB BC

DE DC
C
E
4 x

3 4
3x  16
1
x 5
3
Sum of angles = 360 degrees
A.) Special Quads.
1.) Parallelograms –
Opp. Sides =
Opp. Sides //
Opp. Angles =
Cons. Angles supplementary
2 diagonals bisect each other
2.) Rectangles –
All properties of // -ograms
Diagonals =
All 4 angles = 90 degrees
3.) Squares –
All properties of rectangles
All four sides =
B.) Area formulas –
Parallelogram = bh
Rectangle = lw
Square = s2 or ½ d2
Ex. What is the length of each side of a square whose diagonal
is 10?
10
s
s
10
s
5 2
2
Ex. The length of a rectangle is twice the width. If the
perimeter of the rectangle is the same as the perimeter of a
square with side 6, what is the square of the length of a
diagonal of the rectangle?
d
w
l
P  2w  2l
l  2w
24  2w  2  2w
24  6w
w4
l 8
d 2  4 2  82
d 2  80
d  80  4 5
Ex. If AB = BC and DB = 5, then the area of ABCD =
A
B
5
D
C
ABCD is a square 
1 2
A d
2
1 2
A   5   12.5
2
.