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23 Cards in this Set
 Front
 Back
Polygon Angle Sum Theorem (Theorem 61)

The sum of the measure of the interior angles of an ngon is (n2)180


Corollary to the Polygon AngleSum Theorem

The measure of each interior angle of a regular ngon is [(n2)180]/n


Polygon Exterior AngleSum Theorem (Theorem 62)

The sum of the measures of the exterior angles of a polygon, one at each vertex is 360.


Theorem 63
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 64
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 65
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 66
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 67
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 68
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 69
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 610
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 611
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 612
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 613
If a parallelogram is a rhombus, then its diagonals are what? 
perpendicular
If a parallelogram is a rhombus, then its diagonals are perpendicular. 

Theorem 614
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 615
If a parallelogram is a rectangle, then its diagonals are what? 
congruent
If a parallelogram is a rectangle, then its diagonals are congruent. 

Theorem 616
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 617
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 618
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 619
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 620
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 621
If a quadrilateral is a trapezoid then what two conditions are met? 
1) the midsegment is parallel to the bases
2) the length of the midsegment is half the sum of the length of the bases. 

Theorem 622
If a quadrilateral is a kite, then its diagonals are what? 
perpendicular
If a quadrilateral is a kite, then its diagonals are perpendicular. 