Download Second Semester Topics

Second Semester Topics
Right Triangles – Chapter 8
1
of hypot.
2
long leg = short
3
short leg =




Pythagorean Theorem
Special Right Triangles
Trig Ratios
Angles of Elevation and Depression
2
leg =
hypot.
2
a
c
b
cos x =
c
a
tan x =
b
sin x =
45
a 2
a
45
a
c
30
hypot. = 2 short leg
short leg =
hypot. = leg
c 60
2
opp
)
hyp
adj
(
)
hyp
opp
(
)
adj
c
3
2
longleg
3

(
c
depression
a
x
elevation
b
Quadrilaterals – Chapter 6
Properties of a Parallelogram:
 Opposite sides are parallel.
 Opposite sides are congruent.
 Diagonals bisect each other.
 Consecutive angles are supplementary.
 Opposite angles are congruent.
Tests for Parallelograms:
 Both pairs of opposite sides are parallel.
 Both pairs of opposite sides are congruent.
 Both pairs of opposite angles are congruent.
 Diagonals bisect each other.
 One pair of opposite sides are both parallel and
congruent.
Rhombus
 (all properties of a parallelogram)
 Four congruent sides.
 Diagonals are perpendicular.
 Diagonals bisect angles of rhombus.
Trapezoid
 Exactly one pair of opposite sides parallel.
Isosceles Trapezoid
 Diagonals are congruent.
 Both pairs of base angles are congruent.
Rectangles
 (all properties of a parallelogram)
 Diagonals are congruent.
 Four right angles.
Squares
 (all properties of a parallelogram)
 (all properties of a rectangle)
 (all properties of a rhombus)
Quadrilaterals
Area and Perimeter– Chapter 10
Triangles
Surround Method
1
bh
2
1
A  product of legs in rt 
2
A=
Dissection Method
Note: a, b, and c are sides of ABC
Regular Polygons
1
A  pa
2
where p = perimeter of polygon
and
a = apothem
s2 3
A
for equilateral 
4
Circles
C  2r or d
A  r
A
m
C
360
Area of Sector 
m 2
r
360
Area of Segment =
Area of Sector - Area of 
1
d1d 2
2
Rectangle
A=lw
Square
A = s2 or A 
1 2
d
2
Parallelogram
A  b1h1  b2 h 2
Rhombus
A
1
d1d 2
2
Trapezoid
A=median●height
A
2
Arc Length 
A  s(s  a)(s  b)(s  c)
abc
where s 
2
1
or A  ab sin C
2
With  diagonals
1
h(b1  b 2 )
2
Kite
A
1
d1d 2
2

Surface Area and Volume – Chapter 11
Prisms and Cylinders
Views of a Solid
LA=hp or LA = hC
Nets of Solids
SA=LA + 2B
B = area of base
V=Bh
Similar Solids
Linear Ratio =
Pyramids and Cones
h = height
1
1
LA  lp or LA  lC
2
2
V
A  4 r 2
a

b
1
V  Bh
3
Sphere
C
A
Arcs and Circles

Chords and Tangents
C 1
2
B

Angles and Arcs

Segments and Circles
D
Central angle of circle C
Inscribed angle
m1 = m AB
m2 =
M
H
E
1
m CD
2
R
P
3
r
4
G
K
1
(m MPN - m MN )
2
or m4 + m MN = 180
R
D
r Q
F
AD = AE
AC
AD = AB
W
m5 =
1
(m RS + m TW )
2
Tangent  radius
T
E
AC
5
m4 =
B
C
T
S
N
1
m3 = (m HK - m EG )
2
A
3
4 3
r
3
Circles – Chapter 12

2
Volume Ratio = 
SA=LA+B
C = circumference of base
a

b
Area Ratio = 
l = slant height
p = perimeter of base
a
b
W

S
AF
2
SQ
QT = RQ
QW
(outside)(whole)=(outside)(whole)
Additional Topics
Taxicab Geometry & Spherical Geometry
 Given a statement, be able to determine if it is true
in Euclidean Geometry and/or Taxicab Geometry
 Given a statement, be able to determine if it is true
in plane Geometry and/or spherical Geometry
3D Coordinates & Locus of Points
 Be able to find distance and midpoint in 3D
 Identify 3D coordinates of a prism
 Match a 3D graph to an equation
 Be able to describe a locus of points or identify an
equation that would be satified by a given set of
points
Relationships within Triangles – Chapter 5
If two sides of a triangle are not congruent then the larger angle lies opposite the longer side.
Given the lengths of the sides of a triangle are



a, b, and c and c is the longest side:
c  a  b then the triangle is obtuse.
2
2
2
If c  a  b then the triangle is right.
2
2
2
If c  a  b then the triangle is acute.
If
2
2
2
Triangle Inequality Theorem - The sum of the lengths of any two sides of a triangle is greater than the length
of the third side.
Hinge Theorem - If two sides of one triangle are congruent to two sides of another and if the included angle of
the first triangle is larger than the included of the second triangle then the third side of the
first triangle is longer than the third side of the second triangle.