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Geometry Vocabulary and Conjectures Exam
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Gravity
Terms in this set (83)
point
a location on a plane or line
line
an infinite number of points the go in two directions
plane
an infinite set of points that creates a flat surface
ray
a line that begins at one point and extends indefinitely in one direction
collinear
ponts on the same line
non collinear
points not on the same line
coplanar
points on the same plane
non coplanar
points not one the same plane
line segment
a line that consists of two points called endpoints; all points are collinear
midpoint of a segment
a midpoint divides a segment into two equal segments
bisector of a segment
a line that intersects a segment at its midpoint
angle
a figure that is formed by two rays meeting at a vertex
sides
the legs of an angle
vertex
the central meeting point of an angle
reflex measure of an angle
the largest amount of rotation less then 360 degrees between the two rays
angle addition postulate
if an angle is cut by an angle bisector at the midpoint, then the angles are congruent
congruent angles
when two angles are equal in degree measure
bisector of an angle
when a line cuts an angle in half at the vertex
adjacent angles
angles that share a common side and vertex
right angle
an angle that is equal to 90 degrees
acute angle
an angle that is less then 90 degrees
obtuse angle
an angle that is more than 90 degrees
supplementary angle
a pair of angles that adds up to 180 degrees
complementary angle
a pair of angles that adds up to 90 degrees
vertical angles
angles that share the same vertex; congruent
linear pair of angles
adjacent angles that form a strait line; supplementary
inductive reasoning
reasoning that involves trial and error
deductive reasoning
reasoning that involves logical assumptions and proven facts
linear pair conjecture
linear pairs are supplementary
vertical angles conjecture
vertical angles are congruent
parallel lines
two or more lines in the same plane but never cross
transversal
a line intersecting two or more lines in a plane
median of a triangle
a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
altitude of a triangle
the perpendicular segment form a vertx to the line containing the opposite side
perpendicular bisector of a triangle
a line (or ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side; makes a 90 degree angle
angle bisector conjecture
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle; also those two angles are congruent
concurrent
when a set of lines has a point in common
inscribed
the shape on the inside of another shape
circumscribed
the outer shape in which the inner shape is inscribed
circumcenter
the point of concurrency for a perp. bisector
incenter
the point of concurrency for angle bisectors
orthocenter
the point of concurrency for altitudes
segment addition postulate
If B is between A and C, then AB+BC=AC
angle addition postulate
the angles can be added together if they are adjacent
angle bisector
a line that cuts an angle in half
alternate interior and exterior angles
when two parallel lines are cut by a transversal, the alt. interior angles are congruent, along with the exterior
same side interior and exterior
when two parallel lines are cut by a transversal, the same side interior and exterior angles are congruent
isosceles angle
two sides are equal in length, the base angles are congruent
SSS
side, side, side conjecture
SAS
side angle side conjecture
ASA
angle, side , angle conjecture
SAA
side, angle, angle conjecture
CPCTC
congruent parts of congruent triangles are congruent
triangle
a three sided shape
equilateral triangle
a triangle where all of the sides are congruent
scalene triangle
a triangle where none of the sides are congruent
acute triangle
a triangle where all angles are less then 90 degrees
obtuse triangle
a triangle where all angles are obtuse
right triangle
a triangle where one angle is 90 degrees
triangle sum conjecture
all angles add up to 180 degrees
remote interior angle
The two angles of a triangle nonadjacent to the exterior angle
remote exterior angle
the angle located on the outer edge of a triangle ; is congruent to the two interior angles
isosceles triangle conjecture
the base angles are congruent, and
angle side inequality conjecture
in a triangle, if one angle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle
triangle inequality conjecture
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
interior polygon sum conjecture
the interior angles add up to the number of sides it has minus 2 times 180
exterior angle sum conjecture
is equal to 360
kite
Quadrilateral with 2 pairs of adjacent congruent sides, with perpendicular diagonals
kite non vertex angles conjecture
the non vertex angles are congruent
kite diagonal conjecture
the diagonal angles of a kite are cut by a diagonal
midsegment
segment that connects the midpoints of two sides of a triangle
mid segment of a triangle
A segment connecting the midpoints of 2 sides
mid segment of a trapezoid
The segment that joins the midpoints of the nonparallel opposite sides of a trapezoid.
parallelogram
a quadrilateral whose opposite sides are both parallel and equal in length
parallelogram sides conjecture
the opposite sides of a parallelogram are congruent
parallelogram angles conjecture
the opposite angles of a parallelogram are congruent
consecutive angles conjecture
the consecutive angles are supplementary
rectangle
a parallelogram with four right angles
properties of a rectangle
all angles are right angles and diagonals are equal
1.each pair of opposite sides are equal
2. the diagonals bisect eachother
3. the opposite angles are equal
4. one diagonal divides it into two congruent triangles and two diagonals divides it into two pairs of congruent triangles
rhombus
a parallelogram with four equal sides
properties of a rhombus
1. opposite sides are parallel. 2. all 4 sides are congruent. 3. opposite angles are congruent. 4. any pair of consecutive angles are supplementary. 5. diagonals are perpendicular bisectors of each other 6. diagonals bisect the vertex angles. 7. diagonals divide the rhombus into 4 congruent right triangles
square
a plane rectangle with four equal sides and four right angles
properties of a square
is a rectangular rhombus
1. all four sides are equal
2. opposite pairs of sides are parallel
3. diagonals are equal, are perpendicular to each other, and bisect each other.
4. all the angles are right triangles
5. diagonals intersect the vertices at 45°
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