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Math Review Sheet:
Quadrilateral
Convex Polygon- Polygon in which each interior angle has a measure less than 180 degrees

Diagonal of a Polygon- Any segment that connects two nonconsecutive vertices of the polygon

Quadrilateral- A four sided polygon

Parallelogram- A quadrilateral in which both pairs of opposite sides are parallel

Rectangle- A parallelogram in which at least one angel is a right angle

Rhombus- A parallelogram in which at least two consecutive sides are congruent

Kite- A quadrilateral in which two disjoint pairs of consecutive sides are congruent
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All four sides are congruent
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The parallel sides are called
bases of the trapezoid
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Opposite sides are parallel
B
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Opposite angles congruent
D
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Any pair of consecutive angles are supplementary

Properties of a RectangleA
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Opposite sides congruent
C
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Diagonals bisect each other
E
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All angles are right angles
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Diagonals are congruent

Properties of a KiteA
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Diagonals are perpendicular (form right angles)
C
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One diagonal is the perpendicular bisector of the other
E
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Opposite sides are parallel
B
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Opposite angles congruent
D
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Any pair of consecutive angles are supplementary
A
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Diagonals are perpendicular (form right angles)
C
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One diagonal is the perpendicular bisector of the other
E
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All sides are congruent
G
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Diagonals divide the rhombus into four congruent right angles

Properties of a SquaresA
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Opposite sides congruent
C
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Diagonals bisect each other
E
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Two disjoint pairs of consecutive sides are congruent
B
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One diagonal bisects the pair of opposite
D
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One pair of opposite angles are congruent
F
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Diagonals bisect the angles
H
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Diagonals form four isosceles right triangles (45-45-90 special triangle)

Properties of a Isosceles trapezoidA
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The bases are parallel
C
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The upper base angles are congruent
E
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Any lower base angles are supplementary to any upper base angles

Proving that a Quadrilateral is a Kite:
A
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if one of the diagonals of a quadrilateral is the perpendicular bisector of the other
diagonal —> it is a kite
Proving that a Quadrilateral is a Rhombus:
A
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if either diagonal of a parallelogram bisects two angles of the parallelogram —> it is a
Rhombus

C
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if a quadrilateral is both a rectangle and a rhombus —> it is a square
Proving that a Trapezoid is Isosceles:
A
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if the lower or upper base angles of a trapezoid are congruent—> it is isosceles
C
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• AAS Thm: if there exist a correspondence between the vertices of two triangles such that two
angles and a non included side of one are congruent to the corresponding parts of the other,
then the triangles are congruent
Ratio & Proportion
• Ratio is a quotient of two numbers (5: 3)
• Slope is rise over run in a ratio
• Proportion is an equation stating that two or more ratios are equal (5:15= 15:45)
• In a Proportion containing 4 terms:
• the 1 and the 4 are called- Extremes
• the 2 and the 3 are called- Means
• Thm: in a proportion the product of the means is equal to the product of the extreme
• Thm: if the product of a pair of non zero numbers is equal to the product of another pair of non
zero numbers then either pair of numbers may be the extremes and the other pair the means
of a proportion
• In a Geometric mean the means in a proportion are equal
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• Postulate: (AAA)if there exist a correspondence between the vertices of two triangles such
that the three angles of one triangle are congruent to the three angles of the other triangle
then the triangles are similar
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• Thm: if three or more parallel lines are intersected by two transversals, the parallel lines divide
the transversals proportionally
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Radicals and Quadratic Equations:
√48=√16ₒ3=4√3

Circles
Circumference- π × d d= diameter
Area- π × r2 r= radius
Sector- region bounded by two radii
Chord- line segment joining two points on a circles
two circles are congruent tif they have congruent radii
two or more coplanar circles with the same center are called concentric circles
a point inside a circle circle is an interior point
a point outside a circle is an exterior point
if a point is on a circle its distance from the center is equal to the radius
diameter of a circle is a chord that passes through the center of a circle
Thm: if a radius is perpendicular to a chord it bisects the chord
Thm: if a radius of a circle bisects a chord that is not a diameter then its perpendicular to that
chord
• Thm: the perpendicular bisector of a chord passes through the center of the circle
• Thm: if two chords are equidistant from the center then they are congruent
• Thm: if two chords are congruent then they are equidistant form the center
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Arc
• Arc- made up of two points on a circle and all the points at the circle needs to connect those
two points in its path
• Measure of an Arc- equal the amount of degrees it takes up out of 360
• Central angle- angle whose vertex is on the center of a circle
• Minor arc- an arc whose points are on or between the sides of a central angle
• Major arc- arc whose points are on or outside the sides of a central angle
• Semi circle- an arc whose endpoints are the end points of a diameter
• measure of a minor arc= the measure of the central angle that intercepts the arc
• measure of a semi circle= the measure of the central angle that intercepts the arc
• measure of a major arc= 360 degrees minus the measure of the minor arc

• Thm:if two central angles of a circle are congruent then their intercepted arcs are congruent
• Thm: if two arcs of a circle are congruent then the corresponding central angles are congruent
• Thm: if two central angles of a circle are congruent then the corresponding central angles are
congruent
• Thm:if two chords of a circle are congruent then the corresponding central angles are
congruent
• Thm: if two arcs of a circle are congruent then the corresponding chords are congruent
• Thm: if two chords of a circle are congruent then the corresponding arcs are congruent
Secant and Tangents
Inscribed angle- An inscribed angle is an angle formed by two chords in a circle which have a
common endpoint
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The other two
endpoints define what we call an intercepted arc on the circle
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An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the
intercepted arc
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Chord chord angle- angle formed by two chords that intersect inside a circle 

 
 
thm- the measure of a chord chord angle is ½ the sum of the measures of the arcs intercepted by the chord
chord angle 
secant secant angle thm- the angle made by two secants intersecting outside a circle is half the
difference between the intercepted arc measures
 
secant secant angle-is an angle whose vertex is outside a circle and whose sides determined by two
secants 

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secant tangent angle- an angle whose vertex is outside a circle and whose sides are determined by a secant
and a tangent  

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tangent tangent angle- an angle whose vertex is outside a circle and sides determined by two tangents 

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Altitude - Hypotenuse Thm:
• if an altitude is drawn to the hypotenuse of a right triangle then,
• the two triangles formed are similar to the given right triangle
• the altitude to the hypotenuse is the mean proportional between the segments of the
hypotenuse
• either leg of the given right triangle is the mean proportional between the hypotenuse of
the given right triangle and the segments of the hypotenuse adjacent to that leg
Pythagorean Thm:
a 2 + b 2 = c2
45-45-90:
45-X
45-X
90-X√2
30-60-90:
30-X
60-X√3
90-2X
Trigonometry
SOH CAH-TOA
Sin-Opposite- Hypotenuse
Cosine-Adjacent-Hypotenuse
Tangent-Opposite-Adjacent
• Use regular Sin Cosin Tangent for finding angles and use inverse Sin Cosin Tangent for sides

• Angle of elevation- angle going up
• Angle of depression- angle going down
• don't use vertical angle for this use angle between line of sight and horizontal
Slope
• Thm: the y-form of the equation of a non vertical line is y=mx+b
b= y intercept
m= slope of line
• Thm: the formula for an equation of a horizontal line is y=b
b= the y coordinate of every point on the line
• Thm: the formula for the equation of a vertical line is x=a
a= the x coordinate of every point on the line



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