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Geometry Midterm
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Gravity
Terms in this set (95)
Dimensions of a point
0
Dimensions of a line
1
Dimensions of a plane
2
a point
simplest figure in geometry, a dot, named by capital letter
a line
figure that extends in two directions without ending
segment
all points between two endpoints
ray
one endpoint and one arrow
segment addition postulate
if B lies between A and C, then AB + BC = AC
angle
figure formed by two rays with same endpoint
vertex
where two rays, segments, or sides meet
acute angle
less than 90 degrees
right angle
= to 90 degrees
obtuse angle
greater that 90 and less that 180
straight angle
= to 180 degrees
angle addition postulate
if B lies in the interior of Angle AOC, then Angle AOB = Angle BOC
adjacent angles
two angles that have a common vertex and side but no common interior points
number of points that define a line
2
number of points that define a plane
3 non-collinear
number of points that define a space
4 non-coplanar
conditional statement
if p, then q
inverse
if not p, then not q
converse
if q, then p
contrapositive
if not q, then not p
subsitution
if x = 3 and 2x = y, then 2(3) = y
reflexive
a = a
symmetric
if a = b, then b = a
transitive
if a = b and b = c, then a = c
midpoint theorem
if B is the midpoint of AC, then AB = 1/2AC
angle bisector theorem
if BD is the bisector of Angle ABC, then ABD = 1/2 Angle ABC
complements
two angles that sum to 90 degrees
supplements
two angles that sum to 180 degrees
vertical angles
two angles whose sides form two pairs of opposite rays
perpendicular lines
two line that intersect to form 90 degree angles
vertical angles theorem
vertical angles are congruent
if two lines are perpendicular
they form congruent adjacent angles
if the exterior sides of two adjacent angles are perpendicular
then the angles are complementary
if two angles are supplements to the same angle (or to congruent angles)
then those angles are congruent
if two angles are complements to the same angle (or to congruent angles)
then those angles are congruent
parallel lines
coplanar lines that do not intersect
skew lines
non-coplanar lines that do not intersect
if two parallel planes are cut by a 3rd plane
then the lines of intersection are parallel
if parallel lines are cut by a transversal what special angles are congruent
corresponding, alternate interior
parallel lines are cut by a transversal, what special angles are supplementary
same side interior
if a transversal is perpendicular to one of two parallel lines
then it is perpendicular to the other line also
5 ways to prove lines parallel
1) alternate interior =
2) corresponding angles =
3) same side interior angles supplementary
4) two coplanar lines perpendicular to the same line
5) two lines parallel to that same line
acute triangle
all angles less than 90
right triangle
one angle = 90
obtuse triangle
one angle greater than 90
equiangular triangle
all angles = , all 60 degrees, also acute
scalene triangle
no two sides the same
isosceles triangle
at least two sides =
equilateral triangle
all sides = , all angles 60 degrees
the angles in a triangle sum to
180
if two angles of one triangle are = to two angles in a second triangle, then
the third angles are also =
the exterior angle of a triangle =
the sum of the two remote interior angles
a polygon with 3 sides is a
triangle
a polygon with 4 sides is a
quadrilateral
a polygon with 5 sides is a
pentagon
a polygon with 6 sides is a
hexagon
a polygon with 7 sides is a
heptagon
a polygon with 8 sides is a
octagon
a polygon with 9 sides is a
nonagon
a polygon with 10 sides is a
decagon
a polygon with 12 sides is a
dodecagon
the sum of the angles in a poygon =
180(n-2)
each interior of a regular polygon =
180(n-2) divided by n
the sum of the exterior angles of a polygon
360
each exterior angle of a regular polygon
360/n
5 ways to prove triangles are congruent
SSS, SAS, ASA, AAS, HL
isosceles triangle theorem
if two sides of a triangle are =, then the angles opposite them are also =
isosceles triangle theorem converse
if two angles in a triangle are =, then the sides opposite them are also =
the bisector of the vertex angle of an isosceles triangle is
perpendicular to the base at its midpoint
median of a triangle
vertex to midpoint, always meet IN the triangle
altitude of a triangle
segment from vertex perpendicular to the opposite side (or the line containing the opposite side), acute - in, right - on, obtuse - out
perpendicular bisector
segment perpendicular to the side at its midpoint, meet acute - in, right - on, obtuse - out
if a point lines on a perpendicular bisector, then
the point is equidistant from the endpoint of that segment
if a point lies on the bisector of an angle, then
it is equdistant from the sides of the angle
properties of a parallelogram
opposite sides ||, opposite sides = , opposite angles = , diagonals bisect each other, consecutive angles supplementary
rhombus
a parallelogram with 4 = sides
rectangle
a parallelogram with 4 right angles
square
a parallelogram with 4 = sides and 4 right angles
5 ways to prove a parallelogram
1) both pairs opposite sides ||
2) both pairs opposite sides =
3) both pairs of opposite angles =
4) one pair of sides || and =
5) diagonals bisect each other
if two lines parallel, all the points on one line
are equidistant from the other
a line that contains the midpoint of one side of a triangle and is || to another
contains the midpoint of the third side
a line that connects the midpoints of two sides of a triangle
is || to the third side and 1/2 its length
if 3 || lines cut off = segments on one transversal,
then it cuts of = segments on all transversals
the midpoint of the hypotenuse of a right triangle
is equidistant from the 3 vertices
if an angle in a parallelogram is a right angle,
then that parallelogram is a rectangle
if two consecutive sides of a parallelogram are = ,
then that parallelogram is a rhombus
trapezoid
a quadrilateral with exactly one pair of opposite sides ||
the median of a trapezoid
connects the midpoints of the legs of a trapezoid, it is || to the bases and the length = 1/2(base1 + base2)
exterior angle inequality theorem
the exterior angle of a triangle is greater than each remote interior angle
SAS Inequality Theorem
if two sides of one triangle are = to two sides of a second triangle and the included angle of one triangle is greater than the included angle of the second triangle, then the side opposite the larger angle is longer
SSS Inequality Theorem
if two sides of one triangle are = to two sides of a second triangle and the third side of one triangle is greater than the third side of the second triangle, then the angle opposite the larger side is larger
the sum of two sides of a triangle
must be greater than the third side, a missing side length must be greater than the difference and less than the sum
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