Similar Triangles
Similar
Section 6-3
AA Similarity
AA
If 2 angles of one triangle are
congruent to 2 angles of another
triangle, then the triangles are
similar.
ABC ~ DEF
B
A
E
C
D
F
SSS Similarity
S
Angles of Polygons
Angles
Section 8-1
Interior Angle Sum Thm.
Interior
If a convex polygon has n
sides and S is the sum of
the measures of its interior
angle, then S = 180(n-2).
angle,
Exterior Angle
Geometric
Probability
Section 7-8
Length Probability Postulate
If a point on AB is chosen at
random and C is between A
and B, then the probability
that the point is on AC is
length of AC
length of AB
Areas of Circles
and Sectors
and
Section 7-7
Area of a Circle
Area
r
A =r
2
Area of Sector of a Circle
Area
A
O
B
m AB
2
Area of sector AOB =
r
360
Joke Time
Joke
What flower grows between your
nose
The Law of Sines and
Law of Cosines
Sections 7-6 and
7-7
Law of Sines
sin A sin B sin C
=
=
a
b
c
c
A
B
a
C
Law of Cosines
a = b + c 2bc cos A
2
2
2
b = a + c 2ac cos B
2
2
2
c = a + b 2ab cos C
2
2
2
Area of Regular
Polygons
Section 7-5
apothem a segment that is
drawn from the center of a
regular polygon perpendicular
to a side of the polygon
Area of a Regular Polygon
If a regular polygon has an a
Angles of Elevation
and Depression
Section 7-5
angle of elevation an angle
formed by a horizontal line
and the line of sight to an
object above the level of the
horizontal.
angle of elevation
angle of
Trigonometry
Section 7-4
A trigonometric ratio is a ratio of
sides of a right triangle.
The three most common ratios are
sine, cosine, and tangent.
SOH CAH - TOA
opposite
sine = sin =
hypotenuse
cosin
Area of Trapezoids,
Rhombi, and Kites
Section 7-4
Area of a Rhombus or Kite
1
A = d1d 2
2
d1
d2
Where d1 and d2 are diagonals.
Area of a Trapezoid
b1
1
A = h(b1 + b2 )
2
h
b2
Joke Time
What is Beethov
Special Right
Triangles
Triangles
Section 7-3
45 -45 -90 triangle
45
o
o
o
In a 45 -45 -90 triangle, the
hypotenuse is 2 times as long
as a leg.
O
32
45O 2 x
3 45
x
o
x
o
45O
o
3
45O
30 -60 -90 triang
Special Right
Triangles
Triangles
Section 7-3
45 -45 -90 triangle
45
o
o
o
In a 45 -45 -90 triangle, the
hypotenuse is 2 times as long
as a leg.
O
32
45O 2 x
3 45
x
o
x
o
45O
o
3
45O
30 -60 -90 triang
The Pythagorean
Thm. & Its Converse
Thm.
Section 7-2
Pythagorean Theorem
Pythagorean
In a right triangle, the sum of the
squares of the measures of the legs
equals the square of the measure of
the hyp
Area of
Parallelograms
Section 7-1
Area of a Rectangle
A = bh
Where b = base and
h= height
Area of a Parallelogram
A = bh
Where b = base and
h= height
Area of Triangle
1
A = bh
2
Where b = base and
h=
Geometric Mean &
the Pythagorean Thm.
the
Section 7-1 & 7-2
The geometric mean between 2
positive numbers a and b is the
positive number x where a x
x2 = ab
x = ab
x
=
b
Thm. 7-1
Thm.
If the altitude
Fractals and SelfSimilarity
Section 6-6
iteration - a process of repeating
the same procedure over and over
again.
fractal a geometric figure that is
created using iteration. It is
infinite in structu
Coordinate Proof
Section 6-6
Guidelines for Placing Figures on
a Coordinate Plane
1. Use the origin as a vertex or center.
2. Place at least one side of a polygon on
an axis.
3. Keep the figure within
Trapezoids and
Kites
Kites
Section 6-5
trapezoid a quadrilateral with
exactly one pair of parallel sides
The parallel sides are called bases.
The nonparallel sides are called legs
base
leg
leg
base
is
Parts of Similar
Triangles
Triangles
Section 6-5
Thm. 6.7 Proportional
Perimeters
Perimeters
If 2 triangles are similar, then the
perimeters are proportional to the
measures of corresponding sides.
6
Special Parallelograms
Section 6-4
Thms. 6-9, 6-10, & 6-11
Each diagonal of a rhombus bisects
two angles of the rhombus.
The diagonals of a rhombus are
perpendicular.
The diagonals of a rectangle a
Parallel Lines &
Proportional Parts
Section 6-4
Thm. 6.4 Triangle Proportionality
If a line is parallel to one side of a
triangle and intersects the other 2
sides in 2 distinct points, then it
separat
Proving That a
Quadrilateral is a
Parallelogram
Section 6-3
A quadrilateral is a parallelogram if any
one of the following is true.
Both pairs of opposite sides are parallel.
(Definition)
Both pairs
Similar Polygons
Section 6-2
similar figures when figures have
the same shape but are different
sizes
The symbol
~ means is similar to.
Defn. of Similar Polygons
Two polygons are similar iff
if their
Properties of
Parallelograms
Parallelograms
Section 6-2
quadrilateral a 4-sided polygon
parallelogram a quadrilateral
with both pairs of opposite sides
parallel
Theorems 6-1, 6-2, 6-3
Theorems
Opposit
Proportions
Proportions
Section 6-1
ratio a comparison of 2
quantities
The ratio of a to b can be
expressed as a:b or a
b
where b is not 0.
A special ratio often found in
nature and used by artists an
Inequalities in Triangles
Inequalities
Section 5-5
Exterior Angle Inequality Thm.
Exterior
The measure of an exterior angle of a
The
triangle is greater than the measure
of each of its remote interior
Inverses,
Contrapositives, and
Indirect Reasoning
Section 5-4
negation the denial of a
statement
Ex. An angle is obtuse.
Negation An angle is not
obtuse.
Inverse ~p
~q
An inverse statement can be form
The Triangle Inequality Thm.
The
&
Inequalities Involving 2 Triangles
Section 5-4 and 5-5
Triangle Inequality Thm.
Triangle
The sum of the lengths of any two
sides of a triangle is greater than
the le
Triangle Centers
Section 5-3
Unlike
squares and circles,
triangles have many centers. The
ancient Greeks found four:
incenter, centroid, circumcenter,
and orthocenter.
Centroid
The centroid is formed
Indirect Proof
Section 5-3
Steps for Writing an Indirect
Proof
1.
2.
3.
Assume the conclusion is false.
Show that this assumption leads to a
contradiction of the hypothesis, or some
other fact, such a