Coordinate Geometry
State the point-slope form of a line
y − y1 = m(x − x1)
What is the triangle inequality theorem?
The sum of any two sides of the triangle must be greater than the sum of the third side
What is the equation of a circle? What is the center and radius?
(x − h)2 + (y − k)^2= r2, where (h, k) is the center and r is the radius.
What is the sum of the internal angles of a quadrilateral?
360
What are the coordinates of (x,y) after a reflection across the x-axis?
(x,-y)
Finish the sentence: A midsegment is ___ the length of the third side.
1/2
Give the formula for the area of a sector in a circle.
A = pi * r2 * theta/360
Give one properties sufficient to prove a quadrilateral is a trapezoid
One pair of parallel sides
What are the coordinates of (x,y) after a rotation of 90 counterclockwise about the origin?
(-y,x)
What is the altitude rule? (See image)
What is the relationship between a central angle AB and an inscribed angle x? (see image)
x = 1/2 AB
Give three properties that are sufficient to prove a quadrilateral is a parallelogram
Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, etc.
What are the coordinates of (x,y) after a rotation of 90 clockwise about the origin?
(y, -x)
What is the leg rule (see image)
S1/L1 = L1/H
S2/L2 = L2/H
Give a ratio of segment lengths for a secant and tangent line (see image)
(c)(b) = a^2
Give two properties sufficient to prove a parallelogram is a rectangle
Any one of its angles is a right angle, diagonals are congruent, one pair of consecutive angles are congruent
What formula should you use to find the coordinates of a point P that partitions a line segment from (x1, y1 ) to (x2, y2 ) into an m:n ratio?
P = (x1 + (m)/(m + n) * (change in x), y1 + (m)/(m + n) * (change in y))
What is the Side Splitter Theorem?
If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally. (See image)
Give a ratio for segment lengths in a circle with two secants (see image)
b/a = c/d
Give two properties sufficient to prove a parallelogram is a rhombus
One pair of consecutive sides are congruent, diagonals are perpendicular, either diagonal is an angle bisector