Download 1 - Quia

Geometry L to J Learning Essentials
1.
90
Acute angle
Geo
Angle with measure less than
Adjacent angles
Geo
Angles with a common vertex, common side
and no interior points in common
Angle
Geo
Union of two rays with common end point
that are non-collinear
Bisect
Geo
To cut in two equal parts
Complementary angles
Geo
Two angles with a sum of 90 degrees
Congruent
Geo
Two figures with equal measure
Line
Geo
A series of points that extend in opposite
directions without end
Midpoint
Geo
Point that divides a segment into two equal
parts
Obtuse angle
Geo
Angle with measure greater than
Parallel lines
Geo
Lines in the same plane that don’t intersect
Perpendicular lines
Geo
Two lines that intersect to form right angles
Plane
Geo
A flat surface with no thickness that extends
indefinitely in all directions
Point
Geo
A position in space with no size
Ray
Geo
A part of a line that is bounded by one
endpoint
Right angle
Geo
Angle with measure of
Segment
Geo
A part of a line that is bounded by two
endpoints
Skew Lines
Geo
Non-coplanar lines that do not intersect
Supplementary angles
Geo
Two angles with a sum of 180 degrees
Vertex
Geo
The common endpoint of two rays or
segments
2.
3.
4.
5.
6.
7.
8.
9.
10.
90
11.
12.
13.
14.
15.
16.
90
17.
18.
19.
Geometry L to J Learning Essentials
20.
21.
Vertical angles
Geo
Two non-adjacent angles formed when two
lines intersect
Acute triangle
Geo
Triangle with all acute angles
Altitude
Geo
Equilateral triangle
Geo
Triangle with all sides equal
Isosceles triangle
Geo
Triangle with at least two equal sides
Median (triangle)
Geo
In a triangle, the segment that joins a vertex
and the midpoint of the opposite side
Obtuse triangle
Geo
Triangle with one obtuse angle
Right triangle
Geo
Triangle with a right angle
Scalene triangle
Geo
Triangle with no equal sides
Similar
Geo
Diagonal
Geo
A segment that connects nonconsecutive
vertices of a polygon
Hexagon
Geo
Six sided polygon
Parallelogram
Geo
Polygon with opposite sides that are parallel
Pentagon
Geo
Polygon with 5 sides
Polygon
Geo
Plane figure with segments for sides
Quadrilateral
Geo
Four sided polygon
Regular Polygon
Geo
A polygon with all sides and angles
congruent
Rhombus
Geo
Quadrilateral with 4 equal sides
22.
Any line segment from a vertex
perpendicular to the base, also the
height of a figure
23.
24.
25.
26.
27.
28.
29.
30.
Figures with corresponding angles
congruent and corresponding sides in equal
ratios
31.
32.
33.
34.
35.
36.
37.
Geometry L to J Learning Essentials
38.
Trapezoid
Geo
Quadrilateral with one pair of parallel sides
Cone
Geo
3 -D figure with a circular base and a vertex not in
the same plane as the base
Cylinder
Geo
Three dimension figure with two circles as
bases that are in parallel planes
Net
Geo
2D drawing of a 3D solid
Prism
Geo
Pyramid
Geo
Slant Height
Geo
The altitude of a lateral face of a pyramid
Sphere
Geo
Set of points in space a given distance from
a given point called the center
Surface Area
Geo
The sum of the area of all faces of a figure
Volume
Geo
The number of cubic units it takes to fill a
region
Arc
Geo
Two points on a circle and all the points on
the circle between them
Central angle
Geo
Angle with its vertex at the center of a circle.
Chord
Geo
A segment with its endpoints on a circle
Circle
Geo
Set of points a given distance from a given
point called the center
Inscribed angle
Geo
An angle with its vertex on the circle and its
sides are chords
Secant
Geo
A line that intersects a circle at exactly two
points
Tangent
Geo
A line that intersects a circle at exactly one
point
Alternate exterior angles
Geo
Angles on opposite sides of transversal; on
exterior of lines; nonadjacent
Alternate interior angles
Geo
Angles on opposite sides of transversal; on
interior of lines; nonadjacent
39.
40.
41.
42.
Three dimension figure with polygonal bases
in parallel planes
with the other surfaces as parallelograms
43.
Three dimension figure with polygonal base
and a vertex
not in the plane of the base
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
Geometry L to J Learning Essentials
57.
Angles that are on the same side of a
transversal on the exterior of the
parallel/intersected lines
Consecutive Exterior Angles
Geo
Consecutive Interior Angles
Geo
Corresponding Angles
Geo
Transversal
Geo
A line or segment that intersects two
different lines at different points
Dilation
Geo
A transformation that alters the size of a
figure, but not its shape
Reflection
Geo
A transformation that flips all parts of a figure
over a line
Rotation
Geo
Transformation
Geo
Translation
Geo
Edge
Geo
The straight or curved paths connecting the
nodes
Network
Geo
A combination of nodes connected by edges
Node
Geo
The points/vertices of a network
58.
Angles that are on the same side of a
transversal on the interior of the
parallel/intersected lines
59.
60.
61.
62.
Angles on the same side of the transversal;
one on the interior; one on the exterior; nonadjacent
63.
64.
A transformation that flips all parts of a figure
over two intersecting lines
The moving of all parts of a figure to a new
location
65.
66.
A transformation that slides all parts of a
figure the same distance in the same
direction
67.
68.
69.
70.
71.
Geometry L to J Learning Essentials
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
E
6. Identify Adjacent, Vertical, Complementary
and Supplementary Angles
AB  BC
C
D
D
Adjacent:
EBF , FBG
Vertical:
FBG, CBA
F
C
B
G
A
Complimentary: EBD, DBC
Supplementary: GBF , FBC
7. Pythagorean Theorem
15
12
x
Geometry L to J Learning Essentials
x 2  122  152
x 9
45º
8. 45º - 45º - 90º Special
Right Triangle Theorems
x 2
x
45º
x
9. 30º – 60º – 90º Special
Right Triangle Theorems
30º
2x
x 3
60º
x
10. Find missing side of similar polygons
6cm
5cm
x
5 6

x 8
8cm
x6
2
3
A
47º
11. Triangle Side Inequalities
Name the longest side:
83º
AC
50º
C
B
A
Find the range of the
possible values of x.
8 < x < 18
5
13
67  33  x  180
x  80
A
12. Find the missing angle
B
C
33º
x
xº
67º
B
C
A
13. Find the value of an exterior angle
or a remote interior angle
x = 100
33º
67º
B
xº
C
Geometry L to J Learning Essentials
A
14. 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
15. 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
16. Find the missing angles
68º
x  112
y  68
x
z  112
z
y
17. Find the measure of an interior and
exterior angle of a regular polygon
Octagon
18. 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
19. 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
20. Find the surface area and volume
SA= Surface Area
Geometry L to J Learning Essentials
of a 3D Solid
V = Volume
Prism :
Cone :
SA  Ph  2 B
SA   r   r 2
V  Bh
1
V  Bh
3
Cylinder :
SA  2 rh  2 r 2
Sphere :
V   r 2h
SA  4 r 2
Pyramid :
4 3
V  r
3
1
P B
2
1
V  Bh
3
SA 
21. Find the slant height
12 cm
13cm
10 cm
22. Draw or identify the net/solid given the other
Cube
23. Find measure of an arc
measure of central angle = measure of the arc
24. Find the length of an arc
Length of arc s =
60
2 r
360
B
25. Find the length of a chord
A
AB = 8
5
3
C
26. Find the measure of central
and inscribed angles
80º
Inscribed = 40o
Central = 80o
C
Circumference = 16 in
Area = 64 in 2
27. Find the exact circumference and area
Radius 8 in.
28. List 5 ways to prove triangles congruent
Defn, SSS, SAS, AAS, ASA
m
29. Identify a Transversal Line
line s
p
s
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
32. Midpoint of a segment
-5 -4 -3 -2 -1 0
1
2
3
4
t
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. Point slope form of a line
y  y1  m( x  x1 )
37. Standard form of a line
Ax  By  C
A,B and C are integers and A  0
38. Write the equation of a line given
two points.
( 2, 4 ) and ( 6, - 8)
m = -3
y – 4 = -3( x – 2 )
39. Write the equation of a line given
one point and slope.
m = 8 point ( 3 , -5 )
(y + 5) = 8(x– 3 )
40. Write the equation of a line
3
x  5 so slope = 3/4
4
y=
Parallel or perpendicular to a line
Given point of ( -3, 2 )
Parallel equation is y – 2 =
3
( x  3)
4
Perpendicular equation is y  2   4 ( x  3)
3
41. Draw a network with 6 nodes and 10 edges
A
c
b
C
b
c
a
cos B 
c
b
tan B 
a
sin B 
42. Find the Sine, Cosine and Tangent of an acute angle
B
a
43. Find missing sides and angles using Trig. Functions
14
c
c (sin 40)  14
14
c
sin 40
14
c
.6427
c  21.8
sin 40 
A
c
B
40º
14
C