Download eometry L to J 2008-2009

1
Acute triangle
Geo
Triangle with all acute angles
2
Adjacent angles
Geo
Angles with a common vertex, common side and no
interior points in common
3
Alternate exterior angles
Geo
Angles on opposite sides of transversal; on exterior of
lines; nonadjacent
4
Alternate interior angles
Geo
Angles on opposite sides of transversal; on interior of
lines; nonadjacent
5
Altitude
Geo
6
Angle
Geo
Union of two rays with common end point that are noncollinear
7
Arc
Geo
Two points on a circle and all the points on the circle
between them
8
Bisect
Geo
To cut in two equal parts
9
Central angle
Geo
Angle with its vertex at the center of a circle.
10
Chord
Geo
A segment with its endpoints on a circle
11
Circle
Geo
Set of points a given distance from a given point called
the center
12
Complementary angles
Geo
Two angles with a sum of 90 degrees
13
Cone
Geo
3 -D figure with a circular base and a vertex not in the same
plane as the base
14
Congruent
Geo
Two figures with equal measure
15
Consecutive Exterior
Angles
Geo
Angles that are on the same side of a transversal on the
exterior of the parallel/intersected lines
16
Consecutive Interior
Angles
Geo
Angles that are on the same side of a transversal on the
interior of the parallel/intersected lines
17
Corresponding Angles
Geo
Angles on the same side of the transversal; one on the
interior; one on the exterior; non-adjacent
18
Cylinder
Geo
Three dimension figure with two circles as bases that
are in parallel planes
19
Diagonal
Geo
A segment that connects nonconsecutive vertices of a
polygon
20
Dilation
Geo
A transformation that alters the size of a figure, but not
its shape
Any line segment from a vertex perpendicular to the
base, also the
height of a figure
21
Edge
Geo
The straight or curved paths connecting the nodes
22
Equilateral triangle
Geo
Triangle with all sides equal
23
Hexagon
Geo
Six sided polygon
24
Inscribed angle
Geo
An angle with its vertex on the circle and its sides are
chords
25
Isosceles triangle
Geo
Triangle with at least two equal sides
26
Line
Geo
A series of points that extend in opposite directions
without end
27
Median (triangle)
Geo
In a triangle, the segment that joins a vertex and the
midpoint of the opposite side
28
Midpoint
Geo
Point that divides a segment into two equal parts
29
Net
Geo
2D drawing of a 3D solid
30
Network
Geo
A combination of nodes connected by edges
Node
Geo
The points/vertices of a network
32
Obtuse triangle
Geo
Triangle with one obtuse angle
33
Parallel lines
Geo
Lines in the same plane that don’t intersect
34
Parallelogram
Geo
Polygon with opposite sides that are parallel
35
Pentagon
Geo
Polygon with 5 sides
36
Perpendicular lines
Geo
Two lines that intersect to form right angles
37
Plane
Geo
A flat surface with no thickness that extends indefinitely
in all directions
38
Point
Geo
A position in space with no size
31
39
Polygon
Geo
Plane figure with segments for sides
40
Prism
Geo
41
Pyramid
Geo
42
Quadrilateral
Geo
Four sided polygon
43
Ray
Geo
A part of a line that is bounded by one endpoint
44
Reflection
Geo
A transformation that flips all parts of a figure over a line
45
Regular Polygon
Geo
A polygon with all sides and angles congruent
46
Rhombus
Geo
Quadrilateral with 4 equal sides
47
Right triangle
Geo
Triangle with a right angle
48
Rotation
Geo
A transformation that flips all parts of a figure over two
intersecting lines
49
Scalene triangle
Geo
Triangle with no equal sides
50
Secant
Geo
A line that intersects a circle at exactly two points
51
Segment
Geo
A part of a line that is bounded by two endpoints
52
Similar
Geo
Figures with corresponding angles congruent and
corresponding sides in equal ratios
53
Skew Lines
Geo
Non-coplanar lines that do not intersect
54
Slant Height
Geo
The altitude of a lateral face of a pyramid
55
Sphere
Geo
Set of points in space a given distance from a given
point called the center
Three dimension figure with polygonal bases in parallel
planes
with the other surfaces as parallelograms
Three dimension figure with polygonal base and a
vertex
not in the plane of the base
56
Supplementary angles
Geo
Two angles with a sum of 180 degrees
57
Surface Area
Geo
The sum of the area of all faces of a figure
58
Tangent
Geo
A line that intersects a circle at exactly one point
59
Transformation
Geo
The moving of all parts of a figure to a new location
60
Translation
Geo
A transformation that slides all parts of a figure the
same distance in the same direction
61
Transversal
Geo
A line or segment that intersects two different lines at
different points
62
Trapezoid
Geo
Quadrilateral with one pair of parallel sides
63
Vertex
Geo
The common endpoint of two rays or segments
64
Vertical angles
Geo
Two non-adjacent angles formed when two lines
intersect
65
Volume
Geo
The number of cubic units it takes to fill a region
L to J Concepts
Geometry
Learning Essential
Example Problem with Solution
R
1. Use proper notation to name angles, lines,
segments and rays.
Q
QRS
S
A
B
AB
L
M
ML
C
D
CD
2. Find measures using bisectors
M
C
CM  2.5cm
D
CD = 5 cm
Find CM
L
M
m LMB  70
find m LMA
A
m LMA  35
B
3. Use a protractor to draw an angle
m AFB  60
A
F
B
4. Measure the line segment to the nearest
A
B
1
5
in
16
sixteenth of an inch
5. Identify Parallel and Perpendicular Lines
B
A
AB CD
AB  BC
C
D
6. Identify a Transversal Line
line s
m
p
s
E
7. Identify Adjacent, Vertical, Complementary
Adjacent:
D
F
C
G
B
A
EBF , FBG
and Supplementary Angles
Vertical:
FBG, CBA
Complimentary: EBD, DBC
Supplementary: GBF , FBC
8. Pythagorean Theorem
15
x 2  122  152
x 9
12
x
45º
9. 45º - 45º - 90º Special
Right Triangle Theorems
x 2
x
45º
x
10. 30º – 60º – 90º Special
Right Triangle Theorems
30º
2x
x 3
60º
x
11. Find missing side of similar polygons
6cm
5cm
x
5 6

x 8
8cm
x6
2
3
A
47º
12. Triangle Side Inequalities
Name the longest side:
83º
50º
C
B
A
Find the range of the
possible values of x.
8 < x < 18
5
13
B
AC
x
C
67  33  x  180
x  80
A
13. Find the missing angle
33º
xº
67º
B
C
A
14. Find the value of an exterior angle
or a remote interior angle
x = 100
33º
xº
67º
B
C
A
15. Identify medians, altitudes, angle bisectors
and perpendicular bisectors of a triangle.
median: AE
angle bisector: AD
perpendicular bisector: EG
G
altitude: FB
B
C
CE  EF D
E
F
16. Name all quadrilaterals that fit a given property
Diagonals bisect each other:
Square, Rhombus,
Rectangle, Parallelogram
Diagonals are perpendicular:
Rhombus, Square
One pair of opposite sides
parallel:
Trapezoid
17. Find the missing angles
68º
x  112
y  68
x
z  112
z
y
18. Find the measure of an interior and
exterior angle of a regular polygon
Octagon
19. Find the interior and exterior angle
sum of a polygon( Interior sum =180(n-2) )
9 sides
Interior: 1260
180(9-2)=1260
Exterior: 360
12 cm
20. Find the perimeter and area of a polygon
7 cm
4 cm
Interior: 135
Exterior: 45
Perimeter: 41 cm
6 cm
Area: 56 cm2
16 cm
21. Find the surface area and volume
T = Surface Area
of a 3D Solid
V = Volume
Prism :
Cone :
T  Ph  2 B
V  Bh
T   r   r2
1
V  Bh
3
Cylinder :
T  2 rh  2 r 2
Sphere :
V   r 2h
T  4 r 2
4 3
V  r
3
Pyramid :
1
P B
2
1
V  Bh
3
T
22. Find the slant height
12 cm
13cm
10 cm
23. Draw or identify the net/solid given the other
Cube
24. Find measure of an arc
measure of central angle = measure of the arc
25. Find the length of an arc
Length of arc s =
60
2 r
360
B
26. Find the length of a chord
A
5
3
AB = 8
C
27. Find the measure of central
and inscribed angles
80º
C
Inscribed = 40o
Central = 80o
Circumference = 16 in
Area = 64 in 2
28. Find the exact circumference and area
Radius 8 in.
29. List 5 ways to prove triangles congruent
Defn, SSS, SAS, AAS, ASA
30. Name the special angles formed
by the transversal line
1
4 3
5
6
7 8
given: m 1  100
2
m 2, m 4, m 6, m 7  80
m 3, m 5, m 8  100
Corresponding: 2 & 6, 3 & 8
1 & 5, 4 & 7
Alternate Exterior:2 & 7,1 & 8
Alternate Interior: 3 & 5,4 & 6
Consecutive Interior: 4 & 5
3&6
Consecutive Exterior: 1 & 7
2&8
31. Determine whether lines are parallel
yes, m t
m
70º
110º
t
32. Midpoint of a segment
-5 -4 -3 -2 -1 0
1
2
3
4
5  (4) 1

2
2
5
 2  8 6  10 
,

  (5, 8)
2
 2

A(2,-6) and B(8,-10)
y
5
4
3
2
1
 0  3 4 1   3 5 
,

  , 
2  2 2
 2
x
-5 -4 -3 -2 -1
-1
1
2
3
4
5
-2
-3
-4
-5
33. Distance between two points
7  (2) = 5
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
on a number line
a
b
a b
34. Distance between two points
on a coordinate plane
(6  2) 2  (8  4) 2 = 4 10
A(2,4) and B(6,-8)
y
5
4
(4  0) 2  (0  3) 2  5
3
2
1
x
-5 -4 -3 -2 -1
-1
1
2
3
4
5
-2
-3
-4
-5
35. Slope of a line
A(2,-7) and B(8,5)
m=2
y
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
x
1
2
3
4
5
m= 
3
4
36. Slope intercept form of a line.
y  mx  b
37. Point slope form of a line
y  y1  m( x  x1 )
38. Standard form of a line
Ax  By  C
A,B and C are integers and A  0
39. Write the equation of a line given
two points.
( 2, 4 ) and ( 6, - 8)
m = -3
y – 4 = -3( x – 2 )
40. Write the equation of a line given
one point and slope.
m = 8 point ( 3 , -5 )
(y + 5) = 8(x– 3 )
41. Write the equation of a line
y=
Parallel or perpendicular to a line
3
x  5 so slope = 3/4
4
Given point of ( -3, 2 )
Parallel equation is y – 2 =
3
( x  3)
4
Perpendicular equation is y  2   4 ( x  3)
3
42. Draw a network with 6 nodes and 10 edges
A
43. Find the Sine, Cosine and Tangent of an acute angle
sin B 
b
c
cos B 
a
c
tan B 
b
a
c
b
C
B
a
A
44. Find missing sides and angles using Trig. Functions
14
c
xº
C
18
x  37.9
14
c
 22.8
B
sin 37.9