Congruent Triangles
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Can be proven by
o
SSS � side side side
o
SAS � side angle side
o
ASA � angle side angle
o
AAS � angle angle side (because if we know 2
angles, we can figure out the third, making ASA) hy-acute
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A bisector divided something into 2 equal
parts
o
A=B
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CPCTC � Corresponding Parts of Congruent
Triangles are Congruent
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Perpendicular bisector forms 2 equal 90*
angles
o
<1, <2 are right angles
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All right angles are congruent
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A midpoint cuts the line in half
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Identity/Reflexive Postulate � Everything is
equal to itself
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If 2 sides of a
triangle are congruent, the angles opposite them are congruent.
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If 2 angles of a triangle are congruent, the
sides opposite them are congruent.
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Subtraction Postulate � equals are subtracted
from equals, the results are equal
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Supplements of equal angles are equal
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All points on the perpendicular bisector of a
line segment are equidistant from the endpoints of the line segment
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From a point outside a line, a line can be
drawn perpendicular to the given line
o
BD is perpendicular to AC --- drawn
perpendicular line
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All points on a
perpendicular bisector are equidistant from the endpoint
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All points on the
angle bisector are equidistant to the rays of the angle
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(An exterior angle of
a triangle is equal to the sum of the 2 remote interior angles)
Indirect proofs
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Given
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Write opposite of what you want to prove �
�assuming the opposite of what I want to prove�
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Try to prove something you know is false
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What you wanted to prove � �Because my
assumption led to a contradiction, my assumption must be false�
Quadrilaterals �
not complete. Look at descriptions
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If alternate interior angles are congruent when
lines are cut by a transversal
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If parallel lines are cut by a transversal, the
alternate interior angles are equal
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If one pair of opposite sides are parallel and
congruent, the quadrilateral is a parallelogram
o
Proving a quadrilateral to be a parallelogram
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Vertical angles are equal
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Opposite sides of a parallelogram are equal
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If both pairs of opposite sides of a quadrilateral
are congruent � parallel
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Opposite sides of a rectangle are equal
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If 2 things are equal to the same thing, then they
must be equal to each other.
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If one pair of opposite sides are parallel and
equal, the quadrilateral is a parallelogram
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Whole is greater than any of its parts
Similar Triangles
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Can be proven by
o
2 equal angles
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A.A. theorum
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Proofs
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Corresponding sides of similar triangles are
in proportion
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YT/YR = XY/ZY
o
In a proportion, the product of the means
equals the product of the extremes
o
When 2 adjacent congruent angles are resting
on a straight line, they are both right angles
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Short answers
o
The line joining the midpoint of 2 sides of a
triangle is parallel to the 3rd side and equal to half its length
o
When an altitude is drawn to the hypotenuse of
a right triangle, the altitude is the mean proportion between the 2 segments
of the hypotenuse
o
When an altitude is drawn to the hypotenuse of
a right triangle, the leg is the mean proportional between the whole
hypotenuse and the segment of the hypotenuse near that leg
Circles
Chord � line segment that joins two points on a circle
Secant � line that joins 2 points but continues outside the
circle
Tangent � touches circle in one point
Arcs
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Central angles � vertex is the center
o
Equal to the number of degrees of the arc in front
of it
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Inscribed angle � vertex of angle is on
circumference
o
� its arc
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Inside angle � vertex is inside the circle
o
� the sum of the arcs in front of it and in back
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Outside angle � made up of two secants
o
� the difference of the 2 arcs in front of it
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Tan Chord
o
� arc in front of it
Length
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When two chords intersect in a circle, the product
of their respective segments are equal
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Whole * Outside = Whole * Outside
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