geomentry Unit 2 and 3 Flashcards
Fractional distance with midpoint formula x
x= x1 + k (x2 -x1)
Fractonal distance with midpoint formula y
y = y1+ k (y2- y1)
number line fractional distance
p = a + k ( b - A)
Distance formual derived ?
from tharogream therom
parallel
lines that never touch
keep the same slope, but put in pint slope form
perpendicular lines
lines that intersect at 90
make slope negite and wirite it reciporical nd then put it in point slope form.
circle centered at orign equation
x squared + y squared = radius squared
circle not centered at origin
(x-h) squared + (y-k) squared = radius squared
equilateral triangle
has 3 equal sides
scalenae triangle
no equal sides
isodocles triangle
2 equal sides
triangle enquality theorm
side 1 + side 2 has to be great than side 3 for it to be a tringle?
cpctc
corespoidn parts of congruent triangles are congruent
congruence tranfomations
rotating, refelcting, translating
reflexive property
every trinangle congruent to itself
symetrical property
every congruence statement can be reversed
Transitive property
in a chain of congruence statements the first triangle is congruent to the last triangle .
congruence postulates of triangles
sss, sas, aas, asa
false ongruence postulates
ssa and aaa
simalarity postulates
aa, sas, sss
similar tirangles
have same shape
congruent triangles
havve the same shpe and size
extreme
biggeest and smallest value is cross multiplicatio
means
vaeles between the extrme and values in cross multiplication
colrollories of Isoscels triangle
1 : equalateril triangles are also equliangular, and vice versa
2: Ech angle sin a equlateril triangle measures 60
longest -largest
the longest side of a triangle is opposite to it largest measure
shortest - smallest
the shortest side of a triangle is opposide to its smallest measure
isosoceles trianlges property
if the measure of a triangle is exactly double the measure of one of its interioir anfles then the triangle is isocoles
converse of isoceles triangle theorem
knonw the original
is 2 angles in a triangle are congruent then the sides opposite to those angles are also congruent
median
a line segment that starts from a vertex and them extends to the midpoint of the other side
alititude
a line sengemnt that starts at a vertex and them extexds to the other side of a triangle. Cuts the triangle not n the middle but at 90 degees
ceneroid
point where all 3 medians meet
orthocenter
the line where all 3 altitudes meet
intercenter
point where triangles anlge bisectors meet
circumcenter
point where triangles perpendicular bisectors meeet
midsegement
the midsegemnt of one side of a triangle connected tot he midsegment of a another side of a triangle
