geometry final

Just about everything on the sheet Ms. Modl gave us except for things that you can't put on the computer... like things with segments and stuff.

let me know if anything is wrong or misspelled and I'll fix it!

Terms

undefined, object
copy deck
converse of the perpendicular bisector theorem
if a point is equidistant from the endpoints of a segment, then it lies of the perpendicular bisector of the segment
SSS
3 sides of one triangle are congruent to 3 sides of another triangle
alternate exterior angles theorem
alternate exterior angles are congruent
congruent angles
angles with the same measure
slope-intercept form
y=mx+b
reflex angle
180°< x < 360°
perpendicular lines have:
slopes that are opposite reciprocals
right angle
90°
obtuse angle
90°< x < 180°
HL
hypotenuse & leg of one right triangle is congruent to the hypotenuse & leg of another right triangle
perimeter of rectangle
P=2L+2w
complementary angles
2 angles with a sum of 90°
exterior angle theorem
measure of the exterior angle is equal to the sum of the remote interior angles
area of rectangle
A=lw
area of triangle
A=½bh
centroid theorem
centroid is ²/₃ the distance from the vertex
verticle angles theorem
if ∠a and ∠b are verticle angles, then ∠a is congruent to ∠b
converse of the isosceles triangle theorem
if 2 ∠s of a triangle are congruent, the opposite sides are congruent
inverse
if not p, then not q
SAS
2 sides and the included ∠ of one triangle are congruent to 2 sides and the included ∠ of another triangle
ASA
2 ∠s and the included side of one triangle are congruent to 2 ∠s and the included side of another triangle
CPCTC
corresponding parts of congruent triangles are congruent
parallel lines
coplanar lines that do not intersect
opposite rays
2 rays with a common enpoint
vertical angles
congruent, opposite, nonadjacent angles formed by 2 intersecting lines
triangle midsegment theorem
the midsegment is parallel to the opposite side of the triangle and its length is ½ the length of the opposite side
isosceles triangle theorem
if 2 sides of a triangle are congruent, the opposite angles are congruent
median
segment connecting vertex to the midpoint of the opposite side
linear pair
adjacent angles with a sum of 180°
perimeter of triangle
sum of sides
law of syllogism
if p the q and q then r are true, then p the r is true
incenter theorem
incenter is equidistant from the sides of the triangle
incenter
intersection of the angle bisectors of a triangle; always inside the triangle
circumcenter theorem
circumcenter is equidistant from the vertices of the triangle
skew lines
lines that are not coplanar, not parallel, and do not intersect
slope of horizontal line
y=b
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the sides of the angle
theorem
a statment that can be proven true
coplanar
points on the same plane
converse of the angle bisector theorem
if a point in the interior of an angles is equidistant from the sides of the angle, then it lies on the angle bisector
perimeter of square
P=4s
if a=b, then a+c = b+c
centroid
intersection of the medians of a triangle; always inside the triangle
subtraction property
if a=b, then a−c = b−c
proof
to show a conclusion is true using deductive reasoning
2 lines can be proved parallel by the:
conv. of the corr. ∠s post.; conv. of the alt. int. ∠s thm.; conv. of the alt. ext. ∠s thm; conv. of the same-side int. ∠s thm.
segment
with endpoints
congruent segments
segments with the same length
slope
y₂−y₁ over x₂−x₁
area of square
A=s²
substitution property
if a=b, then b can be substituted for a
slope of vertical line
x=a
midpoint
point that divides a segment into 2 congruent segments
inductive reasoning
conclusion based on patterns; maybe true; conclusion is a conjecture
zero slope
horizontal line
right angle supplmentary theorem
if ∠1 is congruent to ∠2, and ∠1 & ∠2 are supplementary, then ∠1 & ∠2 are right angles
biconditional
p if and only if q
linear pair theorem
if 2 angles form a linear pair, they are supplementary.
angle
formed by two rays with a common endpoint or vertex
orthocenter
intersection of the 3 altitudes of a triangle; may be outside the triangle
right angle congruence theorem
all right angles are congruent
perpendicular lines
lines that intersect at right angles
collinear
points on the same line
line
extends infinitely
circumcenter
intersection of the perpendicular bisectors of the sides of a triangle; may be outside the triangle
third angles theorem
if 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are congruent.
2 angles that share a side and vertex
ray
endpoint at 1 end; extends infinitely at the other
types of proof
2-column; flowchart; paragraph
supplementary angles
2 angles with a sum of 180°
parallel planes
planes that do not intersect
acute angle
0°< x < 90°
converse of the equilateral triangle corollary
if a triangle is equiangular, then it is equilateral
postulate
a statement accepted as true, without proof.
parallel lines have:
the same slope
corresponding angles postulate
corresponding angles are congruent
conditional
if p, then q
contrapositive
if not q, then not p
definition of congruent triangles
corresponding angles and corresponding sides are congruent
converse
if q, then p
altitude
the perpendicular segment from the vertex to the opposite side
congruent complements theorem
if 2 angles are complementary to the same angle, they are congruent.
deductive reasoning
conclusion based on logic, facts, definitions & properties; true; to prove a conjecture true
midsegment
segment that joins midpoints
point-slope form
y−y₁=m(x−x₁)
multiplication property
if a=b, then ac=bc
transitive property
if a=b and b=c then a=c
law of detachment
if p then q is true, and p is true, then q is true
segment bisector
ray, line, or segment that intersects a segment at its midpoint
AAS
2 ∠s and the nonincluded side of one triangle are congruent to 2 ∠s and the nonincluded side of another triangle
symmetric property
if a=b, then b=a
undefined slope
vertical line
Pythagorean Theorem
a²+b²=c²
alternate interior angles theorem
alternate interior angles are congruent
triangle sum theorem
the sum of the angle measures of a triangle is 180°
transversal
line intersecting 2 coplanar lines at 2 different points
perpendicular bisector theorem
if a point is on the perpendicular bisector of a segment, then it is equidistant from the end points of the segment
same-side interior angles theorem
same-side interior angles are supplementary
equilateral triangle corollary
if a triangle is equilateral, then it is equiangular
reflexive property
a=a
congruent supplements theorem
if 2 angles are supplementary to the same angle, they are congruent.
division property
if a=b, then a/c = b/c

102