Chapter 6 Flashcards
Polygon
A closed planed figure formed by 3 or more segments
Triangle
3 sided
Quadrilateral
4 sided
Pentagon
5 sided
Hexagon
6 sided
Septagon/Heptagon
7 sided
Octogon
8 sided
Nonagon
9 sided
Decagon
10 sided
Hendecagon
11 sided
Dodecagon
12 sided
n-gon
n sides
Regular Polygon
Both equilateral and equiangular
Concave
Diagonals on exterior
Convex
Diagonals in interior
Polygon Angle Sum Theorem
The sum of the interior angle measures of a convex polygon with n sides is:
(n-2)180
Polygon Exterior Angle Sum Theorem
The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees
Parallelogram
A quadrilateral with 2 pairs of parallel sides
Parallelogram Theorems
- If a quadrilateral is a parallelogram, then its opposite angles are congruent
- If a quadrilateral is a parallelogram, then its consecutive angles are supplementary
- If a quadrilateral is a parallelogram, then its diagonals bisect each other
- If a quadrilateral is a parallelogram, then its opposite sides are congruent
Conditions for Parallelograms
- Both pairs of opposite sides are parallel
- One pair of opposite sides are parallel and congruent
- Both pairs of opposite sides are congruent
- Both pairs of opposite angles are congruent
- One angle is supplementary to both of its consecutive angles
- The diagonals bisect each other
Rectangle
A quadrilateral with 4 right angles
Properties of Rectangles
- If a quadrilateral is a rectangle, then it is a parallelogram
- If a parallelogram is a rectangle, then its diagonals are congruent
Rhombus
A quadrilateral with 4 congruent sides
Properties of Rhombi
- If a quadrilateral is a rhombus, then it is a parallelogram (rhombus –> parallelogram)
- If a parallelogram is a rhombus, then its diagonals are perpendicular (rhombus –> perpendicular diags.)
- If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles (rhombus –> each diagonal bisects opposite angles)
Square
A quadrilateral with 4 congruent sides and 4 right angles
Properties of Squares
- Square is a parallelogram
- Square is a rectangle
- Square is a rhombus
*Properties apply for all 3
Conditions for Rectangles
- If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle
- If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
Conditions for Rhombuses
- If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus
- If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
- If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus
Kite
A quadrilateral with exactly 2 pairs of congruent consecutive sides
Properties of a Kite
- If a quadrilateral is a kite, then its diagonals are perpendicular
- If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
- Kite –> one diagonal bisects opposite angles
Trapezoid
Quadrilateral with one pair of parallel sides
Isosceles Trapezoid
Trapezoid with congruent legs
Properties of Isosceles Trapezoids
- If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent
- If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles
- A trapezoid is an
isosceles if and only if its diagonals are congruent
Mid-segment of a Trapezoid
A segment whose endpoints are the midpoints of the legs
Trapezoid Mid-segment 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
