Geometry Chapter 6 Theorems And Postulates

Front 1

Polygon Angle- Sum Theorem (Theorem 6-1)

Back 1

The sum of the measure of the interior angles of an n-gon is (n-2)180

Front 2

Corollary to the Polygon Angle-Sum Theorem

Back 2

The measure of each interior angle of a regular n-gon is [(n-2)180]/n

Front 3

Polygon Exterior Angle-Sum Theorem (Theorem 6-2)

Back 3

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

Front 4

Theorem 6-3
If a quadrilateral is a parallelogram, then its what are congruent?

Back 4

opposite sides

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Front 5

Theorem 6-4
If a quadrilateral is a parallelogram, then its what are supplementary?

Back 5

consecutive angles

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Front 6

Theorem 6-5
If a quadrilateral is a parallelogram, then its what are congruent?

Back 6

opposite sides

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Front 7

Theorem 6-6
If a quadrilateral is a parallelogram, then its what bisect each other?

Back 7

diagonals

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Front 8

Theorem 6-7
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off what on every transversal?

Back 8

congruent segments

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Front 9

Theorem 6-8
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a what?

Back 9

parallelogram

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Front 10

Theorem 6-9
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a what?.

Back 10

parallelogram

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

Front 11

Theorem 6-10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a what?

Back 11

parallelogram

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Front 12

Theorem 6-11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a what?

Back 12

parallelogram

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Front 13

Theorem 6-12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a what?

Back 13

parallelogram

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram

Front 14

Theorem 6-13
If a parallelogram is a rhombus, then its diagonals are what?

Back 14

perpendicular

If a parallelogram is a rhombus, then its diagonals are perpendicular.

Front 15

Theorem 6-14
If a parallelogram is a rhombus, then each diagonal bisects what?

Back 15

a pair of opposite angles

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Front 16

Theorem 6-15

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

Back 16

congruent

If a parallelogram is a rectangle, then its diagonals are congruent.

Front 17

Theorem 6-16
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a what?

Back 17

rhombus

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Front 18

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

Back 18

rhombus

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

Front 19

Theorem 6-18
If the diagonals of a parallelogram are congruent, then the parallelogram is a what?

Back 19

rectangle

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Front 20

Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is what?

Back 20

congruent

If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

Front 21

Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are what?

Back 21

congruent

If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

Front 22

Theorem 6-21
If a quadrilateral is a trapezoid then what two conditions are met?

Back 22

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.

Front 23

Theorem 6-22
If a quadrilateral is a kite, then its diagonals are what?

Back 23

perpendicular

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