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# Geometry EOC

### study flashcards

Sum of Interior Angles of a Polygon 180(n-2)
Measure of Each Interior Angle of a Regular Polygon 180(n-2)/n
Sum of Exterior Angles of a Polygon 360
Measure of Each Exterior Angle of a Regular Polygon 360/n
Triangle with no congruent sides scalene
triangle with 2 congruent sides isosceles
triangle with all congruent sides equilateral
triangle with all angles less than 90 degrees acute
triangle with one angle greater than 90 obtuse
triangle with a 90 degree angle right
sum of interior angles of a triangle 180
supplementary angles add up to 180
angles that add up to 90 complementary
Measure of an exterior angle of a triangle equal to the sum of the remote interior angles
segment joining midpoints of a triangle midsegment
properties of a midsegment always parallel to 3rd side, 1/2 the length of the 3rd side, splits triangle into 2 similar triangles
pythagorean theorem a2 + b2 = c2 where c is hypotenuse of right triangle
slope-intercept form y=mx+b where m is slope and b is y-intercept
point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is point on the line
slope y2-y1/x2-x1
collinear on the same line
lines with same slope & different y-intercepts parallel lines
property of perpendicular lines opposite reciprocal slopes, intersect at right angles
Point on a line segment that is equidistant from each endpoint midpoint
transformations that preserve shape and size rigid transformations: reflections, translations, rotations
transformation that uses a scale factor to enlarge or reduce dilation (creates similar figures)
Factor x2 - 3x - 4 (x-4)(x+1)
What is x2 - y2? How do you factor it? difference of squares (x+y)(x-y)
What are the similar triangles theorems? AA, SSS, SAS
What does similar mean? congruent angles, proportional corresponding sides
What's a proportion? 2 equal ratios
What are the congruence theorems for triangles? SAS, AAS, ASA, SSS, HL
What does CPCTC stand for? corresponding parts of congruent triangles are congruent
How do you solve a proportion? Cross multiply: equal ratios have equal cross products
What kind of transformation is (x,y) = (kx,ky) dilation (NOT a rigid motion, NOT an isometry)
isometry rigid motion, same shape, same size, different position
(x,y) = (x+a,y+b) translation, slide
2 reflections over 2 || lines = ? translation
(x,y)=(-y,x) 90 counterclockwise rotation (or 270 clockwise) about the origin
(x,y)=(x,-y) reflection over the x-axis
2 reflections over 2 intersecting lines rotation
(x,y)=(-x,-y) 180 rotation
(x,y)=(-x,y) reflection over y-axis
(x,y)=(y,-x) 270 counterclockwise rotation (or90 clockwise)
(x,y)=(y,x) reflection over line y=x (slope of 1 through the origin)
(x,y)=(-y,-x) reflection over line y = -x (slope of -1 through the origin)
corresponding angles same relationship to transversal and lines that intersect it (congruent when lines are ||)
alternate interior angles on alternate sides of transversal, between the lines that intersect it (congruent when lines are ||)
alternate exterior angles on alternate sides of transversal, outside the lines that intersect it (congruent when lines are ||)
same side interior angles (aka consecutive interior angles) on same side of transversal, between the lines that intersect it (supplementary when lines are ||)
cross section 2D shape formed by slicing a 3D shape
net 2D representation of 3D shape (shows SA of shape)
properties of isosceles triangle 2 congruent sides, 2 congruent base angles, altitude (height) from base to vertex=median=angle bisector
base of triangular prism triangles
height of triangular prism length from triangle to triangle
Triangle inequality theorem the sum of any 2 lengths must be greater than the 3rd
side splitter theorem if a line is drawn inside a triangle that is || to one of the sides, then it divides the sides proportionally
density mass/volume or unit/area
Cavalieri's principle if 2 solids have the same height and cross sectional area at every level, they have the same volume
Equation of a Circle (center-radius form) (x-h)2 + (y-k)2=r2
general form of an equation of a circle x2+y2+ax+by+c=0
how do you convert general form of a circle to center-radius form? complete the square (divide coefficient of x by 2 then square it and add the number to both sides, do the same thing with y)
central angle vertex is center of circle, arc measure=central angle
inscribed angle vertex on circumference, inscribed angle=1/2arc measure, arc measure 2x inscribed angle
triangle inscribed in a circle with one side being the diameter right triangle
angle formed by a radius and tangent line right angle
vertical angle measures formed by 2 intersecting chords (arc1+arc2)/2
measure of angle formed by a chord and a tangent line 1/2 intercepted arc
measure of angle outside a circle formed by tangents and secants (arc1-arc2)/2
chord AB intersects chord CD, dividing the chords into line segments. What is the mathematical relationship of the segnments? ab=cd
opposite angles of an inscribed quadrilateral are ____ supplementary
chords that are equidistant from the center are ____ congruent
a radius that intersects a chord at 90 is _________ segment bisector
sides of an angle outside a circle formed by 2 tangent lines congruent
relationship of sides of an angle formed by a tangent and secant line tangent line squared = exterior segment x whole secant
relationship of sides of an angle formed by 2 secant lines exterior segment x whole secant = exterior segment x whole secant
how do you find the measure of an angle if you have the measures of one of the trig ratios? use the inverse trig ratio (2nd key)
intersection of altitudes of a triangle orthocenter (can be in, on, or outside the triangle)
intersection of medians of a triangle centroid (divides median by 2:1 ratio)
median of a triangle connects vertex to midpoint of opposite side
intersection of perpendicular bisectors of a triangle circumcenter (equidistant from each vertex-that distance is the radius of the circumscribed circle that can be formed around the triangle)
intersection of angle bisectors of a triangle incenter (equidistant from each side of the triangle at 90, used to inscribe a circle inside the triangle)
properties of isosceles trapezoid 2 nonparallel sides congruent, both pairs base angles congruent, diagonals congruent, adjacent interior angles between the bases supplementary
properties of kite 2 pairs adjacent congruent sides, diagonals perpendicular, one diagonal divides into 2 congruent triangles, 1 pair opposite angles congruent, shorter diagonal bisected by the other
area of kite (d1 x d2)/2
properties of parallelogram opposite sides parallel and congruent, opposite angles congruent, diagonals bisect each other, consecutive angles supplementary
properties of rhombus all sides =, diagonals perpendicular, diagonals are angle bisectors
midsegment theorem The segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
Created by: user-1835426
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