Math Semester 1 Final Flashcards
Pythagorean Theorem
a^2+b^2=c^2
Midpoint
Point that divides the segment into two congruent segments
Segment Bisector
Anything that intersects the segment at its midpoint
Midpoint Formula
M = (x1+x2/2, y1+y2/2)
Distance formula
D = square root of (x1-x2)^2 + (y2-y1)^2
Linear Pair
A pair of supplementary adjacent angles.
Vertical Angles
Angles opposite each other. They are congruent.
Conditional Statement
If hypothesis (p), then conclusion (q)
Converse Statement
If conclusion (q), then hypothesis (p)
Inverse Statement
If not hypothesis (p), then not conclusion (q)
Contrapositive Statement
If not conclusion (q), then not hypothesis (p).
Bioconditional Statement
Hypothesis if and only if conclusion
Coincident Lines
Two or more lines that are coplanar and share every point
Skew Lines
Do not intersect and are not coplanar
Slope-Intercept Form
y = mx + b
Standard Form
Ax + By = C
Point-Slope Form
y - y1 = m(x- x1)
What is the shortest distance from a point to a line.
Perpendicular segment
If (a,b) is reflected in the x-axis then its image is the point….
(a, -b)
If (a,b) is reflected in the y-axis then its image is the point….
(-a, b)
If (a,b) is reflected in the line y = x then its image is the point….
(b, a)
If (a,b) is reflected in the line y = -x then its image is the point….
(-b, -a)
Rotation rule for 90° CCW, 270° CW
(-b, a)
Rotation rule for 180° CCW + CW
(-a, -b)
Rotation rule for 270° CCW, 90° CW
(b, -a)
Rotation rule for 360° CCW + CW
(a, b)
How do you find dilation scale factor?
image length/ actual length = k.
Circumcenter
Intersection of perpendicular bisectors
Incenter
Intersection of angle bisectors
Centroid
Center of medians (the segment that connects the midpoint of a leg to the opposite vertex). C = (x1 + x2 + x3/3), (y1 + y2 + y3/3)
Orthocenter
Intersection of altitudes
What are the triangle congruence theorems?
SAS, SSS, ASA, AAS, HL
Circumcenter is where on acute triangles, right triangles, and obtuse tringles?
Acute: Inside
Right: Midpoint on the Hypotenuse
Obtuse: Outside the Triangle
Orthocenter is where on acute triangles, right triangles, and obtuse triangles?
Acute: Inside
Right: On the right angle
Obtuse: Outside and behind the obtuse angle
