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Math midterm
| Question | Answer |
|---|---|
| Point | identifies a location, no size |
| line | never ends, 1D, can measure portion of a line, infinite in length |
| segment | Part of a line with two end point |
| ray | one end point, extends infinitely on one side, still is infinite in length |
| opposite rays | same endpoint and forms a line |
| intersection | two lines can intersect at a point |
| parallel lines | coplanar lines that do not intersect |
| collinear points | on the same line |
| plane | a flat, 2d surface that extends forever |
| coplaner | on the same plane |
| congruent | same size and shape |
| congruent segments | same length |
| segment addition postulate | AB+BC=AC |
| Midpoint of segment | divides a segment into two congruent segments same length |
| segment bisector | a line, ray, or segment that intersects the midpoint of a segment |
| midpoint formula | X1+x2. Y1+y2 M=(—————-,—————-) 2. 2 |
| pythagorean | distance between points 2 2 2 C = a + b |
| distance formula | __________________________ D=/(x2-x1)^2+(y2-y2)^2 |
| Polygon | a figure formed by 3 or more segments (sides) such that: 1)each segment intersects two other segments (one at each endpoint) 2)no two segments with a common endpoint are collinear |
| concave polygon | extended sides that do not cut inside middle/ interior |
| Concave polygon | cuts in the interior ( has dent) |
| acute angle | between 0 and 90 |
| obtuse Angle | between 0 and 180 |
| right angle | exactly 90 |
| straight angle | Exactly 180 |
| degree | way to measure angles |
| angle addition postulate | M<1+M<2=M<ABC |
| Angle bisector | a ray that divides an angle into two congruent segments |
| linear pair | adjacent angles that forms a line |
| Supplementary angles | A pair of angles that add to 180(they dont have to be adjacent) |
| complementary angles | a pair of angles that add to 90 |
| Vertical angles | sides of angle one that are opposite of sides of angle two |
| two point postulate | through any two points there exists exactly one line |
| line-point postulate | a line contains at least two points |
| line intersection postulate | if two lines intersect then their intersection is Exactly one plane |
| three point postulate | through any three noncollinear points there exists exactly one plane |
| Plane-point postulate | a plane contains at least three noncollinear points |
| Plane-line postulate | if two points lie in a plane then the line containing them lies in the plane |
| plane intersection postulate | if two planes intersect then their intersection is a line |
| congruent supplement theorem | if two angles are supplementary to the same angle than they are congruent |
| congruent complement theorem | if two angles are complements to the same angle than they are congruent |
| vertical angle theorum | vertical angles are congruent |
| skew lines | noncoplaner lines that dont intersect |
| parallel lines | coplaner lines that dont intersect |
| linear pair postulate | M<1+M<2=180 |
| Corosponding angles | angles corrosponding on the same side of the transversal |
| alternate interior angles | different sides of trans |
| same side interior angles | consecutive interior angles ( not congruent they are supplementary) |
| parallel lines | same slope |
| Perpendicular line | negative reciprocal slope |
| scalene triangle | no congruent sides |
| isosceles triangle | At least two congruent sides |
| equilateral triangle | three congruent sides |
| acute triangle | equals to 180 |
| Triangle sum theorum | Sum of interior angles in triangle is 180 |
| Corollary | in a right triangle, the two acute angles are complementary |
| Third angle theorem | If Two pairs of angles are congruent in a pair of thriangles than the third angle is congruent |
| similar | same shape but not same side |
| base angle theorem | in an isosceles triangle base angles are congruent |
| Sss | side side side(proves triangles are congruent) |
| HL | hypotenuse-leg only works for right triangles |
| sas | side-angle-side |
| Asa | angle-side-angle |
| aas | angle-angle-side |
| circumcenter theorem | circumcenter is equidistan to vertices (becomes all radi congruent) |
| incenter | intersection of the angle bisectors |
| incenter theorum | equidistance to triangle sides |
| median | the median of a triangle is the segment from vertex to midpoint |
| centroid theorem | the centroid is 2/3 of the way from the vertex |
| centroid | intersection of the medians |
| mdsegment | connects the midpoint |
| midsegment theorem | parallel to the base and 1/2 length of the base |
| triangle inequality theorem | sum of two smaller sides must be greater than the third side |
| triangle | three sides, one triangle formed, sum of interior angles is 180 |
| qualateral | four sides, two triangles formed, sum of interior angles is 360 |
| pentogon | five sides, three triangles formed, sum of interior angles 540 |
| hexagon | six sides, four triangles formed, sum of interior angles is 720 |
| n-gon | n number of sides, n-2 triangles formed, sum of interior angles (n-2)180 |
| equalateral | all sides congruent |
| equlanglar | all of the angles are congruent |
| regular | polygon that is both equilateral and equiangular |
| sum of exterior angles | 360 (number of sides dont mater) |
| dedecagon | n=12 |
| parallelogram | a quadrilateral with both pairs of opposite side parallel |
| horizonal line | slope=0 |
| trapezoid | one pair of opposite sides parallel |
| quadrilateral | four sided polygon |
| parallelogra, | both pairs opposite sides parallel |
| rectangle | four right angles |
| rhombus | has four congruent sides |
| square | four right angles and four congruent sides |
| rhombus | diagonals perpendicular, diagonals are angle bisectors |
| trapezoid | exactly one set of parallel sides (not a parallelogram) |
| isosceles trapezoid | congruent legs |
| midsegment of trapezoid theorem | parrallel to bases and length =average of two bases |
| kite | a quad with two pairs of congruent consecutive sides but opposite sides not congruent ( not a parallelogram) |
| kite theorem | one pair opposite angles congruent |
| CPCt | corrosponding parts of congruent triangles congruent |
| scale factor | ratio of corresponding sides |
| altitude | segment from vertex, perpendicular side ( height= length of altitude) |
| ratio of perimeters | S.F. |
| ratio of areas | (S.F.)^2 |
| AA | angle angle( method for proving triangles similar) |
| property of similar triangles | corrosponding sides of similar triangles are proportional |
| sss | show all three side pairs are preportional |
| triangle proportionality theorem | is a line is parallel to bases, sides are ./; proportionally |
| pythagorean triples | right triangle in which all three sides are integers |
| acute triangle | c^2<a^2+B^2 |
| right triangle | c^2=a^2+b^2 |
| obtuse triangle | c^2>a^2+b^2 |
| triangle inequality | two smaller sides must be greater than the third side |
Created by:
user-1907656
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