Geometry Ch. 6
Terms in this set (21)
a straight line connecting any two vertices of a polygon that are not adjacent
Polygon Interior Angles Sum
Polygon Exterior Angles Sum
The sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360.
A quadrilateral with two pair of parallel sides
Properties of a parallelogram
-opposite sides are parallel
-opposite sides are congruent
-opposite angles are congruent
-consecutive angles are supplementary
-diagonals bisect each other
Diagonals of a parallelogram
-bisect each other
-each diagonal separates the parallelogram into 2 congruent triangles
Conditions of a Parallelogram
-If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
-if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
-if the diagonals of a quadrilateral bisect each other, then the quadrilateral id a parallelogram
-if 1 pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram
A parallelogram with four right angles
diagonals of a rectangle
If a parallelogram is a rectangle, then its diagonals are congruent.
A parallelogram with four congruent sides
Diagonals of a rhombus
-Diagonals are perpendicular
-each diagonal bisects a pair of opposite angles
conditions for rhombi and squares
-If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
- if 1 diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus
- if 1 pair of consecutive sides of a parallelogram are congruent, the parallelogram is a rhombus
- if a quadrilateral is both a rectangle and a rhombus, then it is a square
A quadrilateral with exactly one pair of parallel sides
the parallel sides of a trapezoid
the nonparallel sides of a trapezoid
Two angles that have the base as a side.
a trapezoid with congruent legs
-each pair of base angles are congruent
-diagonals are congruent
Trapezoid Midsegment 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.
a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
-diagonals are perpendicular.
-exactly one pair of opposite angles are congruent.
-consecutive sides are congruent.