Quiz Prep Flashcards
Ways to prove a shape is a parallelogram?
Show both pairs of opposite sides are parallel. Show both pairs of opposite sides are congruent. Show both pairs of opposite angles are congruent. Show one angle is supplementary to both of its consecutive angles. Show the diagonals bisect each other. Show one pair of opposite sides are congruent and parallel.
Convex
A polygon is convex if no line that contains a side of the polygon contains a point in the interior.
Concave
A polygon that is not convex.
Properties of Parallelograms
Opposite sides of parallelograms are congruent. Opposite angles of parallelograms are congruent. Consecutive angles in a parallelogram are supplementary. The diagonals of a parallelogram bisect each other.
Number of sides of a polygon and type of polygon
3: triangle
4: quadrilateral
5: pentagon
6: hexagon
7: heptagon
8: octagon
9: nonagon
10: decagon
12: dodecagon
n: n-gon
Rhombus
Parallelogram that has 4 congruent sides
Rectangle
Parallelogram with 4 right angles
Square
Parallelogram with 4 congruent sides and 4 right angles
Diagonal
Segment that joins 2 non consecutive vertices
Rhombus Corollary
Quadrilateral is a rhombus IFF it has 4 congruent sides
Rectangle Corollary
Quadrilateral is a rectangle IFF it has 4 right angles
Square Corollary
A quadrilateral is a square IFF it is a rhombus and a rectangle
Theorems about Special Parallelograms
A parallelogram is a rhombus IFF its diagonals are perpendicular. A parallelogram is a rhombus IFF each diagonal bisects a pair of opposite angles. A parallelogram is a rectangle IFF its diagonals are congruent
Trapezoid
A quadrilateral with exactly one pair of parallel sides
Bases
parallel sides
Legs
Non-parallel sides
Isosceles Trapezoids
If the legs of a trapezoid are congruent
Midsegment
The segment that connects the midpoints of the legs
Kite
A quadrilateral that has 2 pairs of consecutive congruent sides, BUT opposite sides are not congruent.
Theorems about Trapezoids
If a trapezoid is isosceles then each pair of base angles is congruent. If a trapezoid has a pair of congruent base angles, Then its isosceles trapezoid. A trapezoid is isosceles IFF its diagonals are congruent
Midsegment Theorem for Trapezoids
The mid segment of a trapezoid is parallel to each base and it length is half of the sum of the bases.
Theorems about Kites
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.
