
vector
A quantity that has both direction and magnitude, or size, and is represented by an arrow drawn between 2 points

initial point
starting point of the vector

terminal point
ending point of the vector

component form
 <5,3> (5 units to the right and 3 units up)
 <1,9> (1 unit to the left and 9 units down)

translation
double reflection across 2 parallel lines

coordinate notation
 (x,y) > (x+3, y2) (right 3 and 2 down)
 (x,y) > (x, y+4) (stays the same, up 4)

Line of reflection is the ____________ of the ________________.
Perpendicular bisector, segment joining preimage to image

composition
when 2 or more transformations are combined to produce a single transformation

cross product property
the product of the extremes equals the product of the means

Reciprocal Property
If two ratios are equal then their reciprocals are also equal

means
bottom right and top left

extremes
top left and bottom right

geometric mean of 2 #s
the square root of the product of the 2 #s

When corresponding angle are congruent then ________________.
Corresponding sides are proportional

AA~
Two cooresponding angles congruent in two triangles = similar triangles

SSS~
All three corresponding sides congruent = similar triangles

SAS~
Two corresponding sides sandwhiching one coresponding angle are congruent = similar triangles

If a line parallel to one side of a triangle intersects the other two sides, then ________________.
It divides the two sides proportionally

If a line divides 2 sides of a triangle proportionally, then __________________.
It is parallel to the third side

If 3 parallel lines intersect two transversals, then _______________.
They divide the transversals proportionally

If a ray bisects an angle of a triangle, then __________________.
It divides the opposite side into segments whose lengths are proportional to the lengths of the other 2 sides



Thm. 9.1
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other

Thm. 9.2
If the altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric mean of the lengths of the two segments

Thm. 9.3
If the altitude is drawn to the hypotenuse of a right triangle, then the length of each leg of the right triangle is the geometric mean of the length of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg

Pythagorean Thm. Converse
c squared = a squared + b squared

Solve a right triangle if you know...?
 2 side lengths
 1 side length and 1 acute angle measure

Concentric Circles
Circles that have the same center and different radii

Common internal tangent
intersects the segment that joins the centers of the two circles

Common external tangent
doesn't intersects the segment that joins the centers of the two circles

Find angle created by two chords (internal intersection)
measure angle = (measure of intercepted arc + measure of arc opposite intersected arc)/2

Find angle created by two secants (outer intersection)
measure angle = (measure of larger intercepted arc  measure of smaller intercepted arc)/2

Find the angle created by 1 secant and 1 tangent (outer)
measure angle = (measure of larger intercepted arc  measure of smaller intercepted arc)/2

Find angle created by two tangents (outer)
measure angle = (measure of larger intercepted arc  measure of smaller intercepted arc)/2

