Chapter 6 Flashcards
Polygon
A plane figure formed by three or more segments called sides such that:
- ) each side intersects exactly two other sides, once at each endpoint.
- ) No two sides with a common endpoint are collinear.
Convex Polgon
A polygon such that no line that contains a side of a polygon contains a point in the interior of the polygon.
Concave Polygon
Polygon that is not convex
Diagonal of a Polygon
A segment that joins two nonconsecutive vertices.
Equilateral
All sides congruent
Equiangular
All angles congruent
Polygon Interior Angle Theorem
The sum of the interior angles of a convex n-gon (n-2)180
Corollary to Polygon Interior Angle Theorem
The measure of each interior angle of a regular n-gon (n-2)180/n
Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360
Corollary to Polygon Exterior Angles Theorem
The measure of each exterior angle in a regular n-gon 360/n
Regular Polygon
All sides and angles congruent
Parallelogram
A quadrilateral whose opposite sides are parallel.
Theorem 6.3
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6.4
If a quadrilateral is a parallelogram, then the opposite angles are congruent.
Theorem 6.5
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Diagonals of a Parallelogram Theorem
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6.7
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.8
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.9
If an angle of a quadrilateral is supplementary to both consecutive angles, then the quadrilateral is a parallelogram.
Theorem 6.10
If the diagonals of a quadrilateral bisect each other,then the quadrilateral is a parallelogram.
Theorem 6.11
If one pair of opposite sides of a quadrilateral are BOTH congruent and parallel, then the quadrilateral is a parallelogram.
Rhombus
Parallelogram with 4 congruent sides.
Rectangle
Parallelogram with 4 right angles.
Square
Parallelogram with 4 congruent sides and 4 right angles. (Both a rhombus and rectangle.)
Theorem 6.12
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Theorem 6.13
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
Theorem 6.14
A parallelogram is a rectangle if and only if its diagonals are congruent
Theorem 6.15
A quadrilateral is a rhombus if and only if it has 4 congruent sides
Theorem 6.16
A quadrilateral is a rectangle if and only if it has 4 right angles.
Trapezoid
Quadrilateral with exactly one pair of parallel sides.
Base
Parallel sides
Legs
non-parallel sides
Base Angles
Pair of angles that share a common base.
each trapezoid has two pairs
Isosceles Trapezoid
Trapezoid with congruent legs.
Trapezoid Base Angles Theorem
If a trapezoid is isosceles, then each pair of base angles is congruent.
Trapezoid Diagonals Theorem
If a trapezoid is isosceles, then its diagonals are congruent.
Theorem 6.19
If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.
Theorem 6.20
If a trapezoid has congruent diagonals, then the trapezoid is isosceles.
Midsegment of A Trapezoid
Segment that connects the midpoints of the legs.
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is:
- ) Parallel to each base
- ) Its length is 1/2 the sum of the length of the bases.
