 | Term | Definition |
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Perpendicular |
2 coplanar lines that intersect to form right angles, ⊥ |
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point |
an exact location in space |
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line |
a straight path that extends without end in opposite directions |
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ray |
part of a line that starts at one endpoint and extends forever |
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line segment |
part of a line that extends from one endpoint to another |
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plane |
a perfectly flat surface that extends infinitely in all directions |
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congruent |
having the same shape and size, ≅ |
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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 |
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vertex |
the point where two sides intersect |
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right angle |
an angle that measures exactly 90° |
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acute angle |
an angle that measures less than 90° |
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obtuse angle |
an angle that measures more than 90° |
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straight angle |
an angle that measures exactly 180° |
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complementary angles |
two angles whose sums add to 90° |
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supplementary angles |
two angles whose sums add to 180° |
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skew lines |
lines in a plane that are neither parallel nor intersecting |
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vertical angles |
opposite angles formed by two intersecting lines |
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transversal |
a line that intersects two or more lines |
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circle |
the set of all points in a plane that are the same distance from a given point |
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center of a circle |
the point inside a circle that is the same distance from all of the points on the circle |
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diameter |
line segment that passes through the center of the circle, and whose endpoints lie on the circle |
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polygon |
a closed plane figure formed by two or more line segments |
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side |
a line bounding a geometric figure |
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vertex of a polygon |
on a polygon, the point where two sides intersect |
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regular polygon |
a polygon in which all sides are congruent and all angles are congruent |
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scalene triangle |
a triangle with no congurent sides |
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isosceles triangle |
a triangle with two congruent sides called legs, the non-congruent side is the base |
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equilateral triangle |
a triangle with all congruent sides |
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acute triangle |
a triangle with all acute angles |
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obtuse triangle |
a triangle with one obtuse angle |
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right triangle |
a triangle with one right angle made by the legs. The longest side which is opposite the right angle is the hypotenuse. |
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diagonal |
a segment that is drawn from one vertex to another and is not one of the sides of a polygon |
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radius |
line segment whose endpoints are the center of a circle and any point on the circle |
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parallel |
lines in a plane that do not intersect |
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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 |
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alternate interior angles |
Pairs of non adjacent angles, both interior, and on opposite sides of the transversal. |
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Alternate Exterior angles |
Pairs of non adjacent angles, both exterior, and on opposite sides of the transversal. |
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Same Side Interior angles |
two nonadjacent interior angles that lie on the same side of the transversal. |
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Triangle Sum theorem |
the 3 interior angles of a triangle sum to 180 degrees |
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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 |
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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 |
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Consecutive vertices |
in a polygon two vertices that are endpoints of the same line |
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Consecutive angles |
of a polygon are 2 sides that have a common endpoint |
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Line intersection Postulate |
2 lines intersect in exactly one point |
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Collinear |
describes a set of points that lie along the same line |
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Coordinates |
numbers that give an absolute location of a place |
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Length of a segment |
distance between its endpoints |
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Unique line postulate |
Through 2 points there is exactly one line |
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midpoint of a segment |
point that divides the segment into 2 congruent segments |
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Plane intersection postulate |
2 planes intersect in a line |
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Unique plane postulate |
through and 3 non-collinear points there is exactly one plane |
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Median of a triangle |
Segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side |
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Perpendicular theorem |
if 2 coplanar lines are ⊥ to a third line then they are parallel |
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Transitive prop of parallel lines |
if 2 lines are ll to a third line then the are ll to each other |
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distance |
absolute value of the difference of their coordinates, between 2 coordinates is √(x₁ - x₂ )² + (y₁ - y₂ )² |
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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 |
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Altitude of a triangle |
⊥ segment from a vertex to a line containing the opposite side |
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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 |
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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) |
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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 |
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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 |
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segment bisector |
A line, segment, or ray that goes through a midpoint of a segment. |
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Perpendicular bisector |
A line that is perpendicular to a segment at its midpoint. |
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angle bisector |
a ray dividing a given angle into two congruent angles each half the size of the given angle. |
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convex polygon |
no diagonal contains a point in outside the polygon |
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concave polygon |
at least one diagonal contains a point outside the polygon |
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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 |
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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. |
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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 |
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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 |
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ASA Congruence |
2 ∠s and the included side of one triangle are congruent to 2 ∠s and the included side of another triangle |
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AAS Congruence |
2 ∠s and the nonincluded side of one triangle are congruent to 2 ∠s and the nonincluded side of another triangle |
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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 |
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Parallel lines |
Coplanar lines that will never intersect - they are the same distance apart |
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Intersecting lines |
2 lines that have one common point |
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plane |
A flat surface that extends without end in all directions - determined by 3 points |
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coplanar |
Figures that lie in the same plane. |
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perpendicular |
Two lines are perpendicular if they form 4 right angles |
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Equiangular triangle |
A triangle with 3 congruent sides - also equilateral |
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Parallelogram |
2 sets of parallel sides, 2 sets of congruent sides, opposite angles congruent, diagnals bisect each other, diagnals form 2 congruent triangles |
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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 |
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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 |
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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 |
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trapezoid |
Quadrilateral with exactly one pair of parallel sides. |
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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 |
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kite |
Quadrilateral with 2 pairs of adjacent congruent sides, with perpendicular diagnals |
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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 |
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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. |
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Triangle inequality |
The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side. |
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Hypotenuse |
The side of a right triangle that is opposite the right angle. It is also the longest side. |
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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). |
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corresponding parts |
the sides and angles of 2 triangles that have the same size shape |
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Congruent triangle |
when all pairs of corresponding angles are congruent and all pairs of sides are congruent |
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Similar polygons |
if the corresponding angles are congruent and the corresponding sides are proportional |
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Perimeters of similar polygons |
If 2 polygons are similar, then the ratio of the perimeters is equal to the ratio of their corresponding sides. |
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AA similarity |
if two angles of a triangle are congruent to two angles of another triangle, the triangles are similar |
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SSS similarity |
if 3 sides of 1 triangle are in proportion to 3 sides of another triangle, the triangles are similar |
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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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