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Interactive Glossary

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aalaysia lindsey

on 8 October 2013

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Transcript of Interactive Glossary

Interactive Glossary
ANGLE
The union of two rays with a endpoint, called the vertex.
http://www.mathsisfun.com/angles.html
Table of Contents
Angle
Bisector
Midpoint
Congruence
Constructions
Parallel/Perpendicular
Dilation
Vector
Similarity
Transformations
Circle
Quadrilaterals
Special Right Triangles
Trigonometry
Proofs
Real Life Ex.

Type of Angle Description
Acute Angle: an angle that is less than 90°
Right Angle: an angle that is 90° exactly
Obtuse Angle: an angle that is greater than 90° but less than 180°
Straight Angle: an angle that is 180° exactly
Reflex Angle: an angle that is greater than 180°
Bisector
To divide into two congruent parts.
Midpoint of
Segment
B
A line, ray or segment which cuts
another line
segment into two equal parts
Bisector (segment)
Midpoint
The midpoint splits it into two equal sides
M
A
12x+3
10x+5
12x+3=10x+5
2x=2
x=1
http://www.core-learning.com/downloads/resources/math/geo_apdx1.pdf
The bisector of an angln is the line
or line segment that divides the
angle into two equal parts.
A
Ex: If FH bisects <EFG & m <EFG=120o, what is m<EFH?
Bisector (angles)
D
C
B
BD is an angle bisector <ABC
E
H
G
F
120
2
=
60
m<EFH = 60
Real Life EX.
Midpoint
A point on a line segment that divides the segment into two congruent segments.
c
A
B
Point C bisects
of the
segments of AB
C=[3+(-5)] /2
-5 -4 -3 -2 -1 0 1 2 3 4 5
C=(-2) /2
C=-1
Formula
Real Life
the lower part of his torso is
the midpoint of his elevation
Congruence
Figures or angles that have
the same size and shape.

Real Life
Congruence Mapping
(Isometrics)
It means a mapping which
preserves distances
Corresponding parts
Two triangles are congruent when the three sides and
the three angles of one triangle
have the same measurements as three sides
and three angles of another triangle.
The parts of the two
triangles that have the
same measurements
A theorem: For any points A and B there exists a translation mapping A to B.
A translation is an isometry.The three points A, B and X can be completed in a unique way to a parallelogram or any points X, Y the quadrilateral XY T(Y )T(X) is a parallelogram,since XT(X)||AB||Y T(Y )
Therefore, XY =T(X)T(Y ), so T is isometricry
Proof:
Congruent Triangles
(AAS Theorem): If two angles and a side not between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent
(ASA Postulate): If two angles and the side between
them in one triangle are congruent to the
corresponding parts in another triangle,
then the triangles are congruent
(SSS Postulate): If each side of
one triangle is congruent to the
corresponding side of another
triangle, then the triangles
are congruent
(HL Postulate): If the hypotenuse and
leg of one right triangle are congruent
to the corresponding parts
of another right triangle,
then the triangles are congruent
(LA Theorem): If one leg and an acute angle
of one right triangle are
congruent to the corresponding parts
of another right triangle,
then the triangles are congruent
http://planetmath.org/Congruence.html
Formulas
Congruence formulas obtained by counting irreducible.
Concept of role and competencies
Competency management framework
Competency identification
Competency assessment
Competency development
Expectation of significant others and self
Linking concept
individual
team
organization
Different from position
Skill:
Ability accomplish
Talent:
Inherent ability
Competency:
Constructions
To draw shapes, angles,or lines accurately.
In constructions you use
compass, straightedge
(i.e.ruler) and a pencil.
A compass is a metal
V-shaped tool that
helps draw arcs or circles.
straight edge which can be
used to draw a line segment.
This is another term for the Stitched Fine Edge.In math helps us draw, write, and solve problems
Real Life:
http://www.mathsisfun.com/geometry/constructions.html

Affinities
Circulations
Site Planning
Environment
land use
Zoning

Cost
Labor productivity
Materials
Structure
MEP
Assembly
Systems

Scale
Proportion
Texture & Color
Form
Symbolism
Rhythm
Landscaping
Functions
Technology
Esthetics
What Geometric Construction is in the real word
Parallel/Perpendicular Lines
a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end...
AB
CD
Intersecting - Lines cross or meets
http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm
To better explain
Example
Formulas:
The slope of L1 is and 3/5 . Find the slope of L2 .

Since the lines are perpendicular, the slopes are negative reciprocals.

The slope of L2 is -5/3 . ANSWER
Parallel- describes lines in the same plane that never cross.
The slope of L1 is 3/5 and L1||L2 . Find the slope of L2 .Since the lines are parallel, the slopes are the same.The slope of L2 is also 3/5 . ANSWER
Example
3/5||3/5
Real Life:
Dilation
A dilation is a type of transformation
that changes the size of the image

Real Life
http://www.mathwarehouse.com/transformations/dilations/dilations-in-math.php
In this image the scale factor is 2.
Therefor This dilation means
image A' is twice the size of A
Scale Factor
describe how much the figure
is made bigger or reduced.
Ex. A dilation with scale factor of X, you can find the image of a point by multiplying each coordinate by X: (a ,b) (ka , kB)
http://physics.about.com/od/mathematics/a/VectorMath.htm
Vectors
Its a number physic and geometric applications, which values from its ability to represent magnitude and direction simultaneously.
Real Life:
Wind, for example, had both a speed and a direction and, hence, is conveniently
expressed as a vector. The same can be said of moving objects and forces. The location of a points on a Cartesian coordinate plane is usually expressed as an ordered pair (x, y),
which is a specific example of a vector. Being a vector, (x, y) has a a certain distance
(magnitude) from and angle (direction) relative to the origin (0, 0).
Vectors are quite useful in simplifying problems from three-dimensional geometry.
notation:
In these diagrams magnitude (length) and direction are shown.
The second step in molecular cloning is to join the passenger DNA to the DNA of a suitable cloning vehicle.
These vehicles (or vectors) have the property that they replicate themselves and any attached passenger
DNA so that the passenger is amplified and can be eventually isolated. A number
of different vectors have been developed for genetic engineering. Each has special distinguishing properties..
SuperV
Vectors can also be cloning vectors
V
Formula:
Similarity
Real life:
Two shapes are Similar if the
only difference is size
SSS
Side-Side-Side Similarity - If all pairs of corresponding sides of two triangles are proportional, then the triangles are similar.
SAS
Side-Angle-Side Similarity - If one angle
of a triangle is congruent to one
angle of another triangle and the sides
that include those angles are
proportional, then the two
triangles are similar.
AA
http://hotmath.com/hotmath_help/topics/angle-angle-similarity.html
If two angles of a triangle are
congruent to two angles
of another triangle, then the two
triangles are similar.
Scale Factor
Corresponding sides change by the same scale factor.
all the sides of the small figure are multiplied by the
same number to obtain the lengths of the
corresponding sides of the large figure.
in the picture below
The scale factor of figure A to B is: 3 (3 * 3 = 9; 5 * 3=15)
The scale factor of figure B to A is: 1/3 (9 * 1/3 = 3; 15 * 1/3 = 5)
A transformation consisting of rotations and translations which leaves a given arrangement unchanged.
Transformations
Real Life:
Resizing
dilation, contraction, compression,
enlargement or even expansion
http://www.harcourtschool.com/glossary/math_advantage/images/slide7.gif
Circle
Draw a curve that is "radius" away from a central point.
A movement of a
geometric figure to a new
position without
turning or flipping it
Translation Slide
description: 7 units to the left and 3 units down.
mapping:
notation:
vectors:
v
http://mrsdell.org/geometry/motion.html
Reflection flip
flipping a geometric figure over
a line of reflection to obtain a
mirror image
Rotation turn
A turning of a figure
about a fixed point
Parts of a Circle
http://www.science.co.il/formula.asp
Real Life:
Formula:
for the distance of the circle
A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle.
is to find the surface of the circle
Pythagorean Theorem
Pythagorean Theorem
This proof is by the distinguished Dutch mathematician E. W. Dijkstra (1930 - 2002). The proof itself is, like Proof #18, a generalization of Proof #6 and is based on the same diagram. Both proofs reduce to a variant of Euclid VI.31 for right triangles (with the right angle at C). The proof aside, Dijkstra also found a remarkably fresh viewpoint on the essence of the theorem itself:









If, in a triangle, angles α, β, γ lie opposite the sides of length a, b, c, then sign( + - ) = sign(a² + b² - c²),
where sign(t) is the signum function. BCN = CAB and ACL = CBA so that ACB = ALC = BNC. The details and a dynamic illustration are found in a separate page.
Quadrilaterals
A four-sided figure.
Real Life:
http://www.mathsisfun.com/quadrilaterals.html
Types of quadrilaterals:
Sides: a, b, c, d
Angles: A, B, C, D
Around the quadrilateral are a, A, b, B, c, C, d, D, and back to a, in that order

Altitudes: ha , etc.
Diagonals: p = BD, q = AC, intersect at O
Angle between diagonals: theta

Perimeter: P
Semiperimeter: s
Area: K

Radius of circumscribed circle: R
Radius of inscribed circle: r
Formulas:
Special Right triangles
A special right triangle is a right triangle
with some regular feature that makes
calculations on the triangle easier.
Real life:
https://www.khanacademy.org/math/geometry/right_triangles_topic/special_right_triangles/v/30-60-90-triangle-side-ratios-proof
The 30° and 60° angles give this one away.
x = 6
2x =12
z = x3√=63√
Trigonometry
45 45 90
If we represent the legs of an

isosceles right triangle by 1, we can use the Pythagorean Theorem to establish pattern relationships between the lengths of the legs and the hypotenuse. These relationships will be stated as "short cut formulas" that will allow us to quickly arrive at answers regarding side lengths without applying trigonometric functions, or other means.



There are two pattern formulas that apply ONLY to the 45º-45º-90º triangle.
30 60 90
If you draw an altitude in an equilateral triangle, you will form two congruent 30º- 60º- 90º triangles. Starting with the sides of the equilateral triangle to be 2, the Pythagorean Theorem will allow us to establish pattern relationships between the sides of a 30º- 60º- 90º triangle. These relationships will be stated here as "short cut formulas" that will allow us to quickly arrive at answers regarding side lengths without applying trigonometric functions, or other means.
There are three pattern relationships that we can establish that apply ONLY to a 30º-60º-90º triangle.
The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
Real Life:
Formulas:


They've given me an angle measure and the length of the side "opposite" this angle, and have asked me for the length of the hypotenuse. The sine ratio is "opposite over hypotenuse", so I can turn what they've given me into an equation:



sin(20°) = 65/x

x = 65/sin(20°) Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved

I have to plug this into my calculator to get the value of x: x = 190.047286...



x = 190.047
A theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other
http://mathworld.wolfram.com/PythagoreanTheorem.html
Formula:
Proofs
A geometric proof involves writing reasoned,
logical explanations that
use definitions,
axioms, postulates,
and previously proved theorems to
arrive at a conclusion about a
geometric statement
http://www.basic-mathematics.com/geometry-proofs.html
Since angle C is bisected, angle (x) = angle (y)Segment AC = segment BC ( This one was given) Segment CF = segment CF (Common side is the same for both triangle ACF and triangle BCF)Triangles ACF and triangle BCF are then congruent by SAS or side-angle-side In other words, by
AC-angle(x)-CF and BC-angle(y)-CF Since triange ACF and triangle BCF are congruent, angle A = angle B
By Aalaysia Lindsey
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