6 Flashcards
A parallelogram can be a
Rhombus square rectangle
Figure out a parallelogram
Two pairs of parallel sides
Figure out a rhombus
Opposite reciprocal slopes of diagonals
Figure out a rectangle
Opposite receipt cal slopes
Figure out a square
Rhombus and a rectangle
Figure out a trapeOid
One pair of parallel sides
Figure out an isosceles trapezoid
Distance formula for legs or diagonals have to be congruent
Polygon
A plane figure formed by THREe or more segments called sides
Convex
A polygon that is convex if no line that contains a side of the polygon contains a point in the interior of the polygon
Concave
A polygon that is not convex
Diagonal
A segment of a polygon that joins two non consecutive vertices
Equilateral
A polygon is equilateral if all sides are congruent
Regular
A polygon is regular if it’s both equiangular and equilateral
Polygon interior angle theorem
The sun of the measure of their int angles of a convex ngon is
(n-2)(180)
Corollary 6.1
The measure of each int angle of a regular ngon is 1/2 (n-2) (180)
Polygon ext angle theorom
The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360 degrees
Corollary 6.2
The measure of every exterior angle of a regular ngon is 1/n (360)
Rhombus
Pgram that all four sides re congruent
Rectangle
P gram with four right angles
Square
P gram with for congruent sides and right angles
Thm 6.12
A p gram is a rhombus iff it’s diagonals are perp
Thm 6.13
A p gram is a rhombus iff each diagonal bisects a pair of opposite angles
Thm 6.14
A p gram is a rectangle iff it’s diagonals are congruent
Thm 6.15
A quad is a rhombus iff it has four congruent sides
Thm 6.16
A qua is a rectangle iff it has for right angles
Trapezoid
Has exactly one pair of opposite sides
Isosceles trapezoid
If the legs are congruent than the trapezoid is isosceles
Base angles
A trapezoid has two base angles
Trapezoid base angles theorem
If a trapezoid is isosceles than each pair of base angles is congruent
Trapezoid diagonals theorem
If a trapezoid is isosceles than it’s diagonals are congruent
Thm 6.19
If a trapezoid has one pair of congruent base angles than it is an isosceles trapezoid
Thm 6.20
If a trapezoid has congruent diagonals than it is an isosceles trapezoid
Midsegment
The segment that connects the midpoints of its legs
Midsegment Thm for trapezoid
The Midsegment of a trapezoid is parallel to each base and it’s length is half the sum of the lengths of the bases
