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Geometry 454
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Gravity
For Geometry 454-455
Terms in this set (98)
Perpendicular
2 coplanar lines that intersect to form right angles, ⊥
point
an exact location in space
line
a straight path that extends without end in opposite directions
ray
part of a line that starts at one endpoint and extends forever
line segment
part of a line that extends from one endpoint to another
plane
a perfectly flat surface that extends infinitely in all directions
congruent
having the same shape and size, ≅
angle
a figure formed by two rays with a common endpoint, can be named by the vertex ∠A or by 3 point with the vertex in the middle ∠ABC
vertex
the point where two sides intersect
right angle
an angle that measures exactly 90°
acute angle
an angle that measures less than 90°
obtuse angle
an angle that measures more than 90°
straight angle
an angle that measures exactly 180°
complementary angles
two angles whose sums add to 90°
supplementary angles
two angles whose sums add to 180°
skew lines
lines in a plane that are neither parallel nor intersecting
vertical angles
opposite angles formed by two intersecting lines
transversal
a line that intersects two or more lines
circle
the set of all points in a plane that are the same distance from a given point
center of a circle
the point inside a circle that is the same distance from all of the points on the circle
diameter
line segment that passes through the center of the circle, and whose endpoints lie on the circle
polygon
a closed plane figure formed by two or more line segments
side
a line bounding a geometric figure
vertex of a polygon
on a polygon, the point where two sides intersect
regular polygon
a polygon in which all sides are congruent and all angles are congruent
scalene triangle
a triangle with no congurent sides
isosceles triangle
a triangle with two congruent sides called legs, the non-congruent side is the base
equilateral triangle
a triangle with all congruent sides
acute triangle
a triangle with all acute angles
obtuse triangle
a triangle with one obtuse angle
right triangle
a triangle with one right angle made by the legs. The longest side which is opposite the right angle is the hypotenuse.
diagonal
a segment that is drawn from one vertex to another and is not one of the sides of a polygon
radius
line segment whose endpoints are the center of a circle and any point on the circle
parallel
lines in a plane that do not intersect
corresponding angles
A pair of angles which are on the same side of the transversal, one must be interior, one must be extirior, and they must be nonadjacent
alternate interior angles
Pairs of non adjacent angles, both interior, and on opposite sides of the transversal.
Alternate Exterior angles
Pairs of non adjacent angles, both exterior, and on opposite sides of the transversal.
Same Side Interior angles
two nonadjacent interior angles that lie on the same side of the transversal.
Triangle Sum theorem
the 3 interior angles of a triangle sum to 180 degrees
Angle Addition postulate
if point B lies in the interior of angle AOC, then the m of angle AOB + the m of angle BOC = m of angle AOC
Segment addition postulate
If point B lies between points A and C on line AC then m of AB + m of BC = m of AC
Consecutive vertices
in a polygon two vertices that are endpoints of the same line
Consecutive angles
of a polygon are 2 sides that have a common endpoint
Line intersection Postulate
2 lines intersect in exactly one point
Collinear
describes a set of points that lie along the same line
Coordinates
numbers that give an absolute location of a place
Length of a segment
distance between its endpoints
Unique line postulate
Through 2 points there is exactly one line
midpoint of a segment
point that divides the segment into 2 congruent segments
Plane intersection postulate
2 planes intersect in a line
Unique plane postulate
through and 3 non-collinear points there is exactly one plane
Median of a triangle
Segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
Perpendicular theorem
if 2 coplanar lines are ⊥ to a third line then they are parallel
Transitive prop of parallel lines
if 2 lines are ll to a third line then the are ll to each other
distance
absolute value of the difference of their coordinates, between 2 coordinates is √(x₁ - x₂ )² + (y₁ - y₂ )²
Unequal angles theorem
if 2 angles of a triangle are not congruent, then the sides opposite the larger of the 2 angles is longer than the side opposite the smaller angle
Altitude of a triangle
⊥ segment from a vertex to a line containing the opposite side
unequal sides theorem
if 2 sides of a triangle are not congruent, then the angle opposite the longer side is larger than the angle opposite the smaller side
remote interior angle
it is one of the two other angles of the triangle (with which the exterior angle does not form a linear pair)
Exterior angle of a triangle
the measure of an exterior angle of a triangle is equal to the sum of the 2 remote interior angles
parts of an isosceles triangle
the 2 ≅ sides are legs, the non-congruent side is the base, the angles that formed by the base and a leg are base angles, angle formed by the legs is the vertex angle
segment bisector
A line, segment, or ray that goes through a midpoint of a segment.
Perpendicular bisector
A line that is perpendicular to a segment at its midpoint.
angle bisector
a ray dividing a given angle into two congruent angles each half the size of the given angle.
convex polygon
no diagonal contains a point in outside the polygon
concave polygon
at least one diagonal contains a point outside the polygon
Exterior angle Theorem
In a triangle, the measure of an exterior angle is equal to the sum of the measures of the interior angles at the other two vertices of the triangle - also known as remote interior angles
Isosceles Triangle Theorem
If two sides of a triangle are congruent the angle opposite them are congruent. Conversely, if 2 angles of a triangle are congruent then the sides opposite them must be congruent.
SSS Triangle Congruence postulate
If three sides of one triangle are congruent to three sides of a second triangle then the two triangles are congruent
SAS Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent
ASA Congruence
2 ∠s and the included side of one triangle are congruent to 2 ∠s and the included side of another triangle
AAS Congruence
2 ∠s and the nonincluded side of one triangle are congruent to 2 ∠s and the nonincluded side of another triangle
HL Congruence
if the a leg and the hypotenuse of one right triangle are congruent to the same in another right triangle then the triangles are congruent
Parallel lines
Coplanar lines that will never intersect - they are the same distance apart
Intersecting lines
2 lines that have one common point
plane
A flat surface that extends without end in all directions - determined by 3 points
coplanar
Figures that lie in the same plane.
perpendicular
Two lines are perpendicular if they form 4 right angles
Equiangular triangle
A triangle with 3 congruent sides - also equilateral
Parallelogram
2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles
rhombus
2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 congruent sides, diagnals bisect angles, diagnals perpendicular
rectangle
2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 right angles, diagnals congruent
square
2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles, 4 congruent sides, diagnals bisect angles, diagnals perpendicular, 4 right angles, diagnals congruent
trapezoid
Quadrilateral with exactly one pair of parallel sides.
isosceles trapezoid
one opposite side is parallel, one pair of opposite congruent angles, its base angles are congruent, its consecutive are supplementary, its diagonals are congruent, and it has exactly one line of symmetry
kite
Quadrilateral with 2 pairs of adjacent congruent sides, with perpendicular diagnals
Pythagorean theorem
States that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. a²+b²=c²
use pythagorean theorem to classify triangles
If c²=a²+b² then it is right. If c²>a²+b² then it is obtuse. If c²<a²+b² then it is acute.
Triangle inequality
The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side.
Hypotenuse
The side of a right triangle that is opposite the right angle. It is also the longest side.
included angle
an angle of a triangle that is formed by two sides of the triangle (where each of these sides is equal to a side in the other triangle).
corresponding parts
the sides and angles of 2 triangles that have the same size shape
Congruent triangle
when all pairs of corresponding angles are congruent and all pairs of sides are congruent
Similar polygons
if the corresponding angles are congruent and the corresponding sides are proportional
Perimeters of similar polygons
If 2 polygons are similar, then the ratio of the perimeters is equal to the ratio of their corresponding sides.
AA similarity
if two angles of a triangle are congruent to two angles of another triangle, the triangles are similar
SSS similarity
if 3 sides of 1 triangle are in proportion to 3 sides of another triangle, the triangles are similar
SAS SImilarity
if one angle of a triangle is congruent to an angle of another triangle, and the sides of each triangle adjacent to that angle are in proportion, the triangles are similar
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