Quadrilaterals and Other Polygons Flashcards
The sum of the measures of the n angles in a polygon with n sides is…
(n - 2) x 180
In any polygon, the sum of the exterior angles, taking one at each vertex, is…
360
In any regular polygon the measure of each interior angle is
((n-2)x180)/n
In any regular polygon, the measure of each exterior angle is
360/n
A parallelogram is..
a quadrilateral in which both pairs of opposite sides are parallel.
A parallelograms opposite sides have what property?
The opposite sides of a parallelogram are equal.
The opposite angles of a parallelogram have what property?
The opposite angles of a parallelogram are equal.
The consecutive angles of a parallelogram have what properties?
The consecutive interior angles of a parallelogram add up to 180. Ex: a + b + 180, b + c + 180 , c + d = 180, etc.
When a parallelogram is divided by two diagonals that bisect each other than the two halves of the total line are ?
equal.
A parallelogram that is divided by a diagonal line is split into…
two congruent triangles. (The triangles have the same size and shape.)
In addition to the definition of a parallelogram, what other criteria pertain to rectangles?
- ) the measure of each angel is 90.
2. ) The diagonals of a rectangle have the same length: AC = BD
Not only must squares meet the criteria of a parallelogram and a rectangle, but also these additional criteria…
- ) All four sides have the same length.
- ) Each diagonal divides the square into two 45-45-90 right triangles.
- ) The diagonals are perpendicular to each other.
A trapezoid is a quadrilateral in which…
one pair of sides is not parallel and the other pair of sides is parallel.
The parallel sides of a trapezoid are called…
bases and the bases are never equal.
The nonparallel sides of the trapezoid are..
not equal.
If the non-parallel sides of a triangle are parallel than it is what kind of trapezoid?
An isosceles triangle.
The area formula for a parallelogram is
A = bh
The area formula for a rectangle
a = length x width
The area formula for a trapezoid is…
A = (1/2) (b1 + b2)h
For a given perimeter, a rectangle is in fact a square when…
For a given perimeter, the rectangle with the largest area is a square. For a given area, the rectangle with the smallest perimeter is a square.
If a square is bisected by two lines then each of the triangles created is…
one fourth of the area of the square.
Joining the midpoints of the four sides of any quadrilateral creates…
a parallelogram whose area is one-half the area of the original quadrilateral.
For a given perimeter, the rectangle with the largest area is a …
square
For a given area, the rectangle with the smallest perimeter is a …
square
The area formula of an equilateral paralellogram is..
A = B * H
