Polygons
a geometric shape with many sides
What is a polygon?
A type of quadrilateral where both pairs of opposite sides are parallel and congruent
What is a parallelogram?
The sum of the interior angles in a triangle is equal to 180°
What is the Triangle Angles Sum Theorem?
This theorem states: If a quadrilateral is a parallelogram, then its consecutive interior angles are supplementary.
What is the parallelogram consecutive angles theorem?
The pair of parallel sides in a trapezoid
What are the bases of a trapezoid?
A polygon where all interior angles are less than 180°
What is a convex polygon?
a type of parallelogram with four congruent sides and four right angles.
What is a square?
The sum of the measures of the interior angles of a convex n-gon is (n - 2) × 180.
What is the polygon interior angles theorem?
This theorem states: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
What is the parallelogram diagonals theorem?
The pair of non-parallel sides in a trapezoid.
What are the legs of a trapezoid?
A polygon where all angles are congruent.
What is an equiangular polygon?
a type of parallelogram with four right angles
What is a rectangle?
The sum of the measures of the exterior angles of a convex polygon is 360° (no matter how many sides it has).
What is the polygon exterior angles theorem?
This theorem states: A parallelogram is a rhombus if and only if its diagonals are perpendicular.
What is the rhombus diagonals theorem?
This theorem states: If a trapezoid is isosceles, then each pair of base angles is congruent.
What is the trapezoid base angles theorem?
A polygon where all sides are congruent.
A type of quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Angles found inside a polygon.
What are interior angles?
This theorem states: A parallelogram is a rectangle if and only if its diagonals are congruent
What is the rectangle diagonals theorem.
the midsegment of a trapezoid is parallel to both bases, and is ½ the sum of the lengths of the bases.
midsegment = 1/2( b1 + b2 )
What is the trapezoid midsegment theorem?
A type of polygon that is both equiangular and equilateral.
What is a regular polygon?
A type of quadrilateral that has exactly one pair of parallel sides.
What is a trapezoid?
Angles that form a linear pair with the interior angles of a polygon.
What are exterior angles?
This theorem states: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
What is the rhombus opposite angles theorem?
This theorem states: In an isosceles trapezoid, the diagonals are congruent
What is the isosceles trapezoid diagonals theorem?