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Contrapositive "if A, then B (A -> B)"

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If not B, then not A (~B -> ~A)

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Converse "if A ,then B (A -> B)"

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If B, then A (B->A)

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Inverse "if A , then B (A -> B)"

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If not A, then not B (~A-> ~B)

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Theorem

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a statement that has been proven

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corollary

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a statement that makes sense based on a theorem

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postulate/axiom

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a statement that is accepted as true without proof

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common notion

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A statement that is not officially defined but that is understood to be common sense.

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endpoint

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A point at either end of a line segment or arc, or a point at one end of a ray.

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midpoint

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a point that divides a segment into 2 congruent segments (AB+ BC=AC)

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Segment Addition Postulate

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A postulate stating that if AC+ BC= AB then point C is between points A and B so AC+ CB= AB

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vertex

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endpoint of an angle

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zero angle

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A ray/angle that measures 0 degrees

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straight angle

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an angle that measures exactly 180 degrees

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right angle

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an angle that measures 90 degrees

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acute angle

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an angle that measures less than 90 degrees

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obtuse angle

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An angle that measures more than 90 degrees but less than 180 degrees

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angle bisector

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a ray that divides an angle into two congruent angles

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adjacent angles

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Two angles that share a side and vertex

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supplementary angles

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two angles whose measures have a sum of 180 degrees

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linear pair

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a pair of supplementary angles that are adjacent

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complementary angles

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two angles whose measures have a sum of 90 degrees

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congruent

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Having the same size and shape. β

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Angle Addition Postulate

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if point C lies in the interior of angle AVB then the measure of angle CVB is the measure of angle AVB

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alternate interior angles

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2 angles formed by a transversal that intersects two parallel lines. The angles are on opposite sides of the transversal and inside the parallel lines

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angle of incidence

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The angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.

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angle of reflection

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The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.

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consecutive interior angles

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2 angles formed by a transversal that intersects two parallel lines. The angles are on the same side of the transversal and are inside the parallel lines.

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corresponding angles

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2 nonadjacent angles formed on the same side of a transversal that intersects two parallel lines, with one angle interior and one angle exterior to the lines.

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Law of Reflection

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A law stating that the angle of incidence is congruent to the angle of reflection.

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skew lines

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Lines that are not in the same plane. Skew lines do not intersect, and they are not parallel.

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transversal

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A line, ray, or segment that intersects two or more coplanar lines, rays, or segments at different points.

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Corresponding Angles Theorem

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If a transversal intersects 2 parallel lines, then corresponding angles are congruent

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Alternate Interior Angles Theorem

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if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

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rigid motion

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a transformation applied to a figure that doesn't change its shape or size at any time

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transformations

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scaling, rotation, and reflecting (flipping) objects to change their appearance.

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Translation

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shifting a set of points horizontally, vertically, or in both directions

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rotation

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circular movement around a single fixed point

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reflection

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produces a mirror image

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dialation/stretching

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changing the size of a figure by a scale factor. they are not rigid motions

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Line of Symmetry

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A line that divides a figure into two congruent halves that are mirror images of each other.

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acute triangle

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A triangle with 3 acute angles

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equilateral triangle

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A triangle with 3 congruent sides and 3 congruent angles. they are also isosceles triangles

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isosceles triangle

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a triangle with at least 2 congruent sides.

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obtuse triangle

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a triangle with one obtuse angle

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right triangle

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A triangle that has a 90 degree angle.

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scalene triangle

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a triangle with no congruent sides

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Triangle Inequality Theorem

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the sum of the lengths of any two sides of a triangle is greater than the length of the third side

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interior angles

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angles on the inside of parallel lines cut by a transversal

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exterior angles

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angles on the outside of parallel lines cut by a transversal

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remote interior angles

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the angles of a triangle that are not adjacent to a given exterior angle

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Angle Sum Theorem

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The sum of the measures of the angles of a triangle is 180.

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Third Angles Theorem

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If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

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Exterior Angle Theorem

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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

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exterior angle corollary

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the measure of an exterior angle of a triangle is greater than the measures of the remote interior angles

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congruence transformation

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changes the position of the figure without changing its size or shape

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congruent triangles

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triangles that have their corresponding parts congruent

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CPCTC

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Congruent Parts of Congruent Triangles are Congruent

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Reflexive Property

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A quantity is congruent (equal) to itself. a = a

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Transitive Property

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If a=b and b=c, then a=c. ( If A is congruent to B, and B is congruent to C, then A is congruent to C.)

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Symmetric Property

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If a = b, then b = a. (If A is congruent to B, then B is congruent to A.)

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AAS Theorem (Angle-Angle-Side)

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If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

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ASA Postulate (Angle-Side-Angle)

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If two angles and the included side of one triangle are congruent to the corresponding parts of a another triangle, they are congruent

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SAS Postulate

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If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent

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SSS Postulate

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If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

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Triangle Congruence Postulate

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A statement that proves triangles are congruent without requiring that the measures of all six pairs of corresponding parts be known.

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Proportional

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equal ratios

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ratio

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A comparison of 2 quantities by division. (a,b) or (a/b)

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scale factor

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the ratio of the lengths of two corresponding sides of two similar polygons

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similar

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Figures that have the same shape but not necessarily the same size. ~

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Similar Triangles

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Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional

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AA Similarity Postulate

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If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar

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SAS Similarity Theorem

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If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

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SSS Similarity Theorem

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If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

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Isosceles Triangle Theorem

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If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

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Converse of Isosceles Triangle Theorem

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If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

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longest opposite largest

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the longest side of a triangle is always opposite the angle with the largest measure

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shortest opposite smallest

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the shortest side of a triangle is always opposite the angle with the smallest measure

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altitude of a triangle

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a perpendicular segment from a vertex to the line containing the opposite side

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Centroid

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the point where the three medians of a triangle meet

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median of a triangle

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a segment from a vertex to the midpoint of the opposite side

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Orthocenter

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The point where the altitudes of a triangle meet

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Triangle w/ the Same Median and Altitude Theorem

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If a line dividing a triangle is both its altitude and its median, the triangle is an isosceles triangle

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circumcenter of a triangle

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The center of the only circle that can be circumscribed about a given triangle.

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Incenter

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The center of the circle inscribed in a triangle

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Midsegment

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a segment connecting the midpoints of two sides of a triangle

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perpendicular bisector

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a segment, ray, line, or plane that bisects a line segment at a right angle

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Triangle Midsegment Theorem

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If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long.

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Triangle Proportionality Theorem

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If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

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Converse of the Triangle Proportionality Theorem

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if a line divides 2 sides of a triangle proportionally, then it is parallel to the third side

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Cross Products Property

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The product of the extremes of a proportion is equal to the product of the means

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convex

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curved outward

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concave

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curved inward

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decagon

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10 sided polygon

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dodecogon

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12 sided polygon

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heptagon

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7 sided polygon

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nonagon

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9 sided polygon

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sum= (n-2) 180

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formula for finding the sum of measures of interior angles of polygons with n sides

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360

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the sum of the exterior angles of a convex, regular polygon

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360/measure of exterior angle

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formula for finding the number of sides a regular, convex polygon

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consecutive angles

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angles that share a side

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Parallelogram

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a quadrilateral whose opposite sides are both parallel and equal in length

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Properties of a parallelograms

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opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, any pair of consecutive angles are supplementary

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rectangle

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a quadrilateral with four right angles (all angles are congruent)
are parallelograms
diagonals are congruent

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adjacent

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near, next to, adjoining

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square

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a quadrilateral with four right angles and four congruent sides
have all properties of parallelograms, rectangles, and rhombi

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Rhombus Properties

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all sides are congruent, diagonals are perpendicular, diagonals bisect opposite angles

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Trapezoid

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A quadrilateral with exactly one pair of parallel sides

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isosceles trapezoid

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a trapezoid with congruent legs and congruent base angles

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median of a trapezoid

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the line segment joining the midpoints of the legs of a trapezoid
parallel to the base

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Trapezoid Properties

answer

the bases are parallel, legs are non parallel, base angles are formed by the base and legs
median is parallel to the bases and the length is equal to half the sum of the bases

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Isosceles Trapezoids Properties

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legs are congruent, both pairs of base angles are congruent, diagonals are congruent

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vertical angles

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A pair of opposite congruent angles formed by intersecting lines

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Vertical Angles Theorem

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If two angles are vertical, then they are congruent

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zero-dimensional

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Having no length, width, or height.
A point

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one-dimensional

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Having length but no width or height.

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two-dimensional

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having height and width

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three-dimensional

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having height, width, and depth

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Coplanar

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points that lie on the same plane

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Collinear

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points that lie on the same line

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((n-2)180)/n)

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formula for finding one interior angle of a regular convex polygon