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Geometry Reference Sheet Chapter 7 2016-2017
Definitions
Base Angles (7.5)
Diagonal (7.1)
Equiangular Polygon (7.1)
Equilateral Polygon (7.1)
Isosceles Trapezoid (7.5)
Kite (7.5)
Midsegment of a trapezoid (7.5)
Parallelogram (7.2)
Rectangle (7.4)
Regular Polygon (7.1)
Rhombus (7.4)
Square (7.4)
Trapezoid (7.5)
In a trapezoid, two consecutive angles whose common side is a base.
A segment in a polygon that joins two nonconsecutive vertices.
All angles in the interior of the polygon are congruent.
All sides are congruent.
A trapezoid with congruent legs.
A quadrilateral that has two pairs of consecutive congruent sides and has
opposite sides which are not congruent.
The segment connecting the midpoints of the legs.
A quadrilateral with both pairs of opposite sides parallel.
A parallelogram with four right angles.
A convex polygon that is both equilateral and equiangular.
A parallelogram with four congruent sides.
A parallelogram with four congruent sides and four right angles.
A quadrilateral with exactly one pair of parallel sides, called the bases.
Theorems and Corollaries
Isosceles Trapezoid Base Angles
Theorem (7.5)
Isosceles Trapezoid Diagonals
Theorem (7.5)
Kite Diagonals Theorem (7.5)
Kite Opposite Angles Theorem
(7.5)
Opposite Sides Parallel and
Congruent Theorem (7.3)
Parallelogram Consecutive
Angles Theorem (7.2)
Parallelogram Diagonals
Theorem (7.2/7.3) (& converse)
Parallelogram Opposite Angles
Theorem (7.2/7.3) (& converse)
Parallelogram Opposite Sides
Theorem (7.2/7.3) (& converse)
Polygon Exterior Angles Theorem
(7.1)
Polygon Interior Angles Theorem
(7.1)
(Corollary to the) Polygon
Interior Angles Theorem (7.1)
Rectangle Corollary (7.4)
Rectangle Diagonals Theorem
(7.4)
Rhombus Corollary (7.4)
Rhombus Diagonals Theorem
(7.4)
Rhombus Opposite Angles
Theorem (7.4)
Square Corollary (7.4)
Trapezoid Midsegment Theorem
(7.5)
A trapezoid is isosceles if and only if each pair of base angles is congruent.
A trapezoid is isosceles if and only if its diagonals are congruent.
If a quadrilateral is a kite, then its diagonals are perpendicular.
If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
If one pair of opposite sides of a quadrilateral is congruent and parallel, then the
quadrilateral is a parallelogram.
If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary.
A quadrilateral is a parallelogram if and only if its diagonals bisect each other.
A quadrilateral is a parallelogram if and only if its opposite angles are congruent.
A quadrilateral is a parallelogram if and only if its opposite sides are congruent.
The sum of the measures of the exterior angles of a convex polygon, one at each
vertex, is
.
The sum of the measures of the interior angles of a convex n-gon is
.
The sum of the measures of the interior angles of a quadrilateral is
.
A quadrilateral is a rectangle if and only if it has four right angles.
A parallelogram is a rectangle if and only if its diagonals are congruent.
A quadrilateral is a rhombus if and only if it has four congruent sides.
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite
angles.
A quadrilateral is a square if and only if it has four congruent sides and four right
angles.
The midsegment of a trapezoid is parallel to each base, and its length is one-half
the sum of the lengths of the bases.
Geometry Reference Sheet Chapter 7 2016-2017