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23 Cards in this Set

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Polygon Angle- Sum Theorem (Theorem 6-1)
The sum of the measure of the interior angles of an n-gon is (n-2)180
Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is [(n-2)180]/n
Polygon Exterior Angle-Sum Theorem (Theorem 6-2)
The sum of the measures of the exterior angles of a polygon, one at each vertex is 360.
Theorem 6-3
If a quadrilateral is a parallelogram, then its what are congruent?
opposite sides

If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6-4
If a quadrilateral is a parallelogram, then its what are supplementary?
consecutive angles

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Theorem 6-5
If a quadrilateral is a parallelogram, then its what are congruent?
opposite sides

If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6-6
If a quadrilateral is a parallelogram, then its what bisect each other?
diagonals

If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6-7
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off what on every transversal?
congruent segments

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Theorem 6-8
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a what?
parallelogram

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Theorem 6-9
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a what?.
parallelogram

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
Theorem 6-10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a what?
parallelogram

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6-11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a what?
parallelogram

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6-12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a what?
parallelogram

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram
Theorem 6-13
If a parallelogram is a rhombus, then its diagonals are what?
perpendicular

If a parallelogram is a rhombus, then its diagonals are perpendicular.
Theorem 6-14
If a parallelogram is a rhombus, then each diagonal bisects what?
a pair of opposite angles

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
Theorem 6-15

If a parallelogram is a rectangle, then its diagonals are what?
congruent

If a parallelogram is a rectangle, then its diagonals are congruent.
Theorem 6-16
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a what?
rhombus

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a what?.
rhombus

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.
Theorem 6-18
If the diagonals of a parallelogram are congruent, then the parallelogram is a what?
rectangle

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is what?
congruent

If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.
Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are what?
congruent

If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.
Theorem 6-21
If a quadrilateral is a trapezoid then what two conditions are met?
1) the mid-segment is parallel to the bases
2) the length of the mid-segment is half the sum of the length of the bases.
Theorem 6-22
If a quadrilateral is a kite, then its diagonals are what?
perpendicular

If a quadrilateral is a kite, then its diagonals are perpendicular.