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1

synthetic proof

proof built using a system of postulates & theorems in which the prop's of figures, but not their actual measurements r studied

2

justifications of synthetic proof

given statements

definitions

postulates

previously proved theorems

3

Bisecting Diagonals Th

If the 2 diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

4

implications

if-then statements that can be represented by symbols

Ex: p → q reads "If p, then q"

5

logically equivalent

either both true or both false

original & contrapositive

6

not logically equivalent

just cuz original = true, doesn't mean converse & inverse r too

7

converse

q → p

If q, then p

8

inverse

~p → ~q

If not p, then not q

9

contrapositive

~q → ~p

If not q, then not p

10

median (of triangle)

a segment joining a vertex to the midpt of the opp. side

11

coordinate proof

a proof based on a coord. system in which all pts r represented by ordered pairs of #'s

12

justifications for coordinate proof

distance & midpt formulas

parallel lines have the same slope

perp. lines have slopes tht r neg. reciprocals of each other

a geometric figure may be placed anywhere in the coord. plane

13

distance formula

14

midpt formula

15

Isosceles Median Theorem

in an isosceles triangle, the medians drawn to the legs r equal in measure

16

isosceles trapezoid

a trapezoid w/ a line of symmetry that passes through the midpts of the bases

17

Isosceles Trapezoid Theorem

In an isosceles trapezoid:

  1. the legs r equal in measure
  2. the diagonals r equal in measure
  3. the 2 angles @ each base r equal in measure

18

inclusive definition

a definition that includes all possibilites

19

exclusive definition

a definition that excludes some possibilities 

20

quadrilateral chart

21

past postulates & theorems

Addition, Subtraction, Mult, Div Prop's of Eq Post's

Reflexive Prop of Eq Post

Substitution Property Post

Distributive Prop. Post

If 2 angles r supp's of same angle, then r equal in measure

if 2 angles r complements of same angle, then equal in measure

Straight Angle Post - if the sides of an angle form a straight line, then the angle is a straight angle w/ measure 180o

Angle/Segment Addition Post - For any seg or angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts

vertical angles r equal in measure

the sum of the measures of the angles of a triangle is 180o

an exterior angle of a triangle is equal in measure to the sum of the measures of its 2 remote interior angles

if 2 sides of a triangle r equal in measure, then the angles opp those sides r = in measure

if 2 angles of a triangle r =, then the sides opp those angles r =

If a tri is equilateral, then is also equiangular, w/ three 60o angles

If a tri is equiangular, then its also equilateral

if 2 parallel lines r intersected by a trans, then corr angles r =, vv

If 2 parallel lines r intersected by a trans, then alt int angles r =, vv

If 2 parallel lines r intersected by a trans, then co-int angles r supp, vv

If 2 lines r perp to the same trans, then they r parallel

If a trans = perp to one of 2 parallel lines, then its perp to the other one also

Thru a pt not on a given line, there's 1 and only 1 parallel line to the given line

If a pt is the same distance from both endpts of a segment, then it lies on the perp bisector of the seg

A seg can be drawn perp to a given line from a pt not on the line

AA similarity - if 2 angles of 1 tri r = to 2 angles of another tri, then the 2 tri's r similar

If a line is drawn from a pt on 1 side of a tri parallel to another side, then it forms a tri similar to the original tri

In a tri, a segment that connects the midpts of 2 sides is parallel to the 3rd side & half as long

ASA, AAS th's

SAS, SSS Post's

If the alt = drawn to the hyp of a right tri, then the 2 triangles formed r similar to the original tri & to each other

Pythagorean Th

If the alt is drawn to the hyp of a right tri, then the measure of the alt is the geometric mean b/w the measures of the parts of the hyp

the sum of the lengths of any 2 sides of a tri is greater than the length of the 3rd side

in an isosc tri, the medians drawn to the legs r equal in measure

in a parallelogram, the diagonals have the same midpt

In a rectangle, the diagonals r equal in measure

In a kite, the diagonals r perp to each other

in a parallelogram, opp sides r equal in measure

If a quadrilateral is a parallelogram, then consecutive angles r supp

If a quad is parallelogram, then opp angles r =

the sum of the measures of the angles of a quad = 360o

if both pairs of opp angles of a quad r equal in measure, then the quad = a parallelogram

 

22

Interior Angle Measures in Polygons Th

the sum of the angle measures of an n-gon is given by the formula

S(n) = (n - 2)180o

23

exterior angle measures in polygons th

the sum of the exterior angle measures of an n-gon, 1 angle at each vertex, is 360o

24

regular polygon

iff all its sides r equal in measure & all its angles r = in measure

25

inscribed

drawn inside the figure

26

circumscribed

drawn outside the figure

27

chords

segments whose endpoints are on the circle

28

Perpendicular bisector of a chord th

The perp bisector of a chord of a circle passes thru the center of the circle

29

central angle

an angle w/ its vertex @ the center of the circle

measure of an arc intercepted (cut off) by a central angle = the measure of that central angle

30

minor arc

< 180

can be named with 2/3 letters (just remember that a major arc is named w/ 3 letters to distinguish it from a minor arc w/ the same endpts)