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Geometry EOC
study flashcards
| Question | Answer |
|---|---|
| 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 |
| adjacent supplementary angles | linear pair |
| 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. |
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