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18 Cards in this Set

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Slope Formula
m= y₂-y₁/x₂-x₁
Distance Formula
d= Γ(x₂-x₁)2+(y₂-y₁)2

Γ=square root
2=squared
CONDITIONAL: (p->q)
Inverse
Converse
Contrapositive
Inverse (~p->~q) F
Converse (q->p) F
Contrapositive (~q->~p) T
[logical equivalent]
Midpoint Formula
(x,y)=(x+x/2,y+y/2)
If 2 triangles are similar, what 5 things must be in proportion?
sides
medians
altitudes
bisectors
perimeters
Special Right Triangles
30-60-90 THEOREM: In a 30-60-90 triangle, if the length of the shorter leg is x, then the hypotenuse is 2x and the longer leg is xΓ3
{x, 2x, xΓ3}

45-45-90 THEOREM: In an isosceles right triangle, if the length of a leg is x, then the other lef is s x and the hypotenuse is xΓ2
{x, x, xΓ2}
Mean Proportional
The mean proportional of 2 numbers 'a' and 'b' is the positive number 'x' such that
a/x = x/b

OR x=Γab
Mean Proportional Theorem
IN A RIGHT TRIANGLE, IF AN ALTITUDE IS DRAWN TO THE HYPOTENUSE:

1) The 2 triangles created by the altitude are similar and both are similar to the original right triangle.

2) The altitude drawn is the mean proportional to the 2 parts of the hypotenuse
{x/part1 = part2/x}

3) The leg of the original right triangle is the mean proportional to the part of the hypotenuse adjacent and the whole hypotenuse.
{leg/adjpart=hyp/leg}
Γx*Γx=
Γx*Γx=x
(Γx)2=z
If x2+x2=y2, then y


(2=squared)
y=xΓ2
Alternate Interior Angles Theorem
If two parallel lines are cut by a
transversal, then the alternate interior angles are congruent.
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Hypotenuse Leg Theorem
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Rotations
90`
180`
270'
1) The measure of the angle of rotation is POSTIVE when the roation is COUNTER-CLOCKWISE

2) The measure of the angle rotation is NEGATIVE when the rotation is CLOCKWISE

R90`(x,y)=(-y,x)
180`(x,y)=(-x,-y)?
R270`(x,y)=(y,-x)
Reflection y=x
Ry=x(x,y)=(y,x)
Transversal
A line that cuts across a set of lines or the sides of a plane figure. Transversals often cut across parallel lines.
Isosceles Trapezoid
2 sides congruent, 2 sides diff
Angle Bisector
Divides the angle into two equal parts.