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Larson Geometry Reference – Chapter 7
Definitions
Term/Concept
Base Angles, Trapezoid
*Bases, Trapezoid
*Diagonal
Equiangular Polygon
*Equilateral Polygon
*Kite
*Legs, Trapezoid
*Median, Trapezoid
(Midsegment)
*Parallelogram
*Polygon
*Quadrilateral
*Rectangle
*Regular Polygon
*Rhombus
Description
Two consecutive angles whose common side is a base.
The parallel sides of a trapezoid.
The diagonal of a polygon is a segment that connects any two nonadjacent verticies.
A polygon in which all interior angles are congruent.
A polygon in which all sides are congruent.
A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not
congruent.
The non-parallel sides of a trapezoid.
The segment that joins the midpoints of its legs.
A quadrilateral with two pairs of opposite sides that are parallel.
A closed plane figure with three or more sides.
Four sided polygons
A parallelogram with four right angles.
A polygon that is both equilateral and equiangular.
A parallelogram with four congruent sides.
*Square
*Trapezoid
A parallelogram with four right angles and four congruent sides.
A quadrilateral with exactly one pair of parallel sides.
*Trapezoid, Isosceles
A trapezoid whose legs are congruent (see theorems 6-14 and 6-15)
Larson Geometry Reference – Chapter 7
Theorems
Theorems
Corollary to the Polygon
Interior Angles Theorem
Isos. Trap. Base Angles
Isos. Trap. Base Angles
Converse
Isos. Trap. Congruent
Diagonals
Kite Opposite Angles
Kite Perpendicular Diagonals
*Polygon Interior Angles
Theorem
*Polygon Exterior Angles
Theorem
*Parallelogram Bisecting
Diagonals Theorem
*Parallelogram Consecutive
Angles Theorem
Parallelogram Opposite Angles
Theorem
Parallelogram Opposite Sides
Theorem
Parallelogram Test: Diagonals
Converse
Parallelogram Test: Opposite
Angles Converse
Parallelogram Test: Opposite
Sides Converse
Parallelogram Test Opposite
Sides Parallel and Congruent
*Rectangle Corollary
*Rectangle Diagonals
*Rhombus Corollary
Rhombus Diagonals
Rhombus Opposite Angles
*Square Corollary
*Trapezoid. Median
(midsegment)
The sum of the measures of the interior angles of a convex quadrilateral is 360.
If a trapezoid is isosceles, then both pairs of base angles of are congruent.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
A trapezoid is isosceles if and only if its diagonals are congruent. The diagonals of an isosceles
trapezoid are congruent.
If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
If a quadrilateral is a kite, then its diagonals are perpendicular.
The sum of the measures of the interior angles of a convex n-gon is 180(n-2) where n is the number
of sides.
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is
360.
The diagonals of a parallelogram bisect each other.
Consecutive angles in a parallelogram are supplementary.
Opposite angles of a parallelogram are congruent.
Opposite sides of a parallelogram are congruent
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a
parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a
parallelogram.
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral
is a parallelogram.
A parallelogram is a rectangle if and only if it has four right angles.
A parallelogram is a rectangle if and only if the diagonals are congruent.
A quadrilateral is a rhombus if and only it has four congruent sides.
A parallelogram is a rhombus if and only if the diagonals are perpendicular.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
A parallelogram is a square if and only if it is a rhombus and a rectangle.
The median (midsegment) of a trapezoid is parallel to the bases, and its measure is one-half the
sum of the measures of the bases.