coordinate geo

2 line segments bisect

2 line segments bisect

have same midpoint- midpoint x2

2 lines are perp

neg recip slopes- slope x2

2 lines are para

same slope- slope x2

line is a perp bisector

bisected+perp- midpoint of the line being bisected, slope of both lines

alt of a triangle

perpendicular- slope x2

median of a triangle

pass thru midpoint- midpoint

isos triangle

2 sides are cong- dist x2-3

right triangle

prove 2 sides are perp- slope x2, Pythagorean thm- dist x3

cong triangles

sss- dist x6

similar triangles

show proportions- dist x6

parallelogram

• 2 sets opp sides are cong- dist x4

• 2 sets opp sides are para- slope x4

• 1 set opp sides are para and cong- dist x2 + slope x2

• diagonals bisect each other- midpoint x2

rectangle

• 4 right angles- slope x4

• para→ right angle- slope x2

• para→ diagonals are cong- dist x2

rhombus

• 4 cong sides- dist x4

• para→ consec sides are cong- distx2

• para→ diagonals are perp- slope x2

square

• rectangle→consec sides→rhombus- distx2

• rectangle→perp diagonals→rhombus- slope x2

• rhombus→one right angle→rectangle- slope x2

• rhombus→cong diagonals→rectangle- dist x2

trapezoid

only one set of opp para sides- slope x4

isos trapezoid

• trap→non-para sides are cong→isos- dist x2

• trap→diagonals are cong→isos- dist x2

standard form slope

-a/b

standard form x/y int

• x: ax=c

• y: by=c