Studied by 9 people
Diagonal
a segment that connects any two nonconsecutive vertices
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is (n-2)*180
Corollary to the Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a quadrilateral is 360 degrees
equilateral polygon
a polygon with all sides congruent
equiangular polygon
a polygon in which all angles are congruent
regular polygon
a convex polygon that is both equilateral and equiangular
Polygon exterior angles theorem
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°
Parallelogram
a quadrilateral with both pairs of opposite sides parallel
Parallelogram opposite sides theorem
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Parallelogram opposite angles theorem
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Parallelogram Consecutive Angles Theorem
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Parallelogram Diagonals Theorem
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Parallelogram opposite sides converse
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Parallelogram opposite angles converse
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Opposite sides parallel and congruent theorem
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.
Parallelogram diagonals converse
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
quadrilateral
a four-sided polygon
Pentagon
5 sided polygon
Hexagon
6 sides
heptagon/septagon
a polygon with 7 sides
Octagon
a polygon with 8 sides
nonagon
polygon with 9 sides
decagon
a polygon with 10 sides
Hendecagon
11 sided polygon
Dodecagon
12 sided polygon
Rhombus
A parallelogram with four congruent sides
rectangle
A parallelogram with four right angles
Square
A parallelogram with four congruent sides and four right angles.
Rhombus Corollary
A quadrilateral is a rhombus if and only if it has four congruent sides
Rectangle Corollary
A quadrilateral is a rectangle if and only if it has four right angles
Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
Rhombus Diagonals Theorem
A parallelogram is a rhombus if and only if its diagonals are perpendicular
Rhombus Opposite Angles Theorem
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
Rectangle Diagonals Theorem
A parallelogram is a rectangle if and only if its diagonals are congruent.
Trapezoid
A quadrilateral with exactly one pair of parallel sides
Isosceles trapezoid
a trapezoid in which the legs are congruent
Isosceles trapezoid base angles theorem
If a trapezoid is isosceles, then each pair of base angles is congruent
Isosceles trapezoid base angles converse
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
Isosceles trapezoid diagonals theorem
A trapezoid is isosceles if and only if its diagonals are congruent.
midsegment of a trapezoid
a segment that connects the midpoints of the legs of a trapezoid
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
Kite
a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
Kite Diagonals Theorem
If a quadrilateral is a kite, then its diagonals are perpendicular.
Kite Opposite Angles Theorem
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
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Flashcard (63)