Postulates & Theorems - chapter 6

Question 1

POLYGON ANGLE SUM THEOREM: The sum of the interior angle measures of a convex polygon with n sides is ….

Answer 1

(n - 2)180 degrees. (theo. 6-1-1)

Question 2

POLYGON EXTERIOR ANGLE SUM THEOREM: The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is ….

Answer 2

360 degrees. (theo. 6-1-2)

Question 3

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

Answer 3

congruent. (theo. 6-2-1)

Question 4

If a quadrilateral is a parallelogram, then its opposite angles are ….

Answer 4

congruent. (theo. 6-2-2)

Question 5

If a quadrilateral is a parallelogram, then its consecutive angles ….

Answer 5

are supplementary. (theo. 6-2-3)

Question 6

If a quadrilateral is a parallelogram, then its diagonals ….

Answer 6

bisect each other. (theo. 6-2-4)

Question 7

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral ….

Answer 7

is a parallelogram. (theo. 6-3-1)

Question 8

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral ….

Answer 8

is a parallelogram. (theo. 6-3-2)

Question 9

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

Answer 9

is a parallelogram. (theo. 6-3-3)

Question 10

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

Answer 10

is a parallelogram. (theo. 6-3-4)

Question 11

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

Answer 11

is a parallelogram. (theo. 6-3-5)

Question 12

If a quadrilateral is a rectangle, then ….

Answer 12

it is a parallelogram. (theo. 6-4-1)

Question 13

If a parallelogram is a rectangle, then its diagonals ….

Answer 13

are congruent. (theo. 6-4-2)

Question 14

If a quadrilateral is a rhombus, then ….

Answer 14

it is a parallelogram. (theo.(6-4-3)

Question 15

If a parallelogram is a rhombus, then its diagonals ….

Answer 15

are perpendicular. (theo. 6-4-4)

Question 16

If a parallelogram is a rhombus, then each diagonal ….

Answer 16

bisects a pair of opposite angles. (theo. 6-4-5)

Question 17

If one angle of a parallelogram is a right angle, then the parallelogram is ….

Answer 17

a rectangle. (theo. 6-5-1)

Question 18

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

Answer 18

a rectangle. (theo. 6-5-2)

Question 19

If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is ….

Answer 19

a rhombus. (theo. 6-5-3)

Question 20

If the diagonals of a parallelogram are perpendicular, then the parallelogram ….

Answer 20

is a rhombus. (theo. 6-5-4)

Question 21

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

Answer 21

is a rhombus. (theo. 6-5-5)

Question 22

If a quadrilateral is a kite, then its diagonals ….

Answer 22

are perpendicular. (theo. 6-6-1)

Question 23

If a quadrilateral is a kite, then exactly one pair of opposite angles ….

Answer 23

are congruent. (theo. 6-6-2)

Question 24

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

Answer 24

are congruent. (theo. 6-6-3)

Question 25

If a trapezoid has one pair of congruent base angles, then ….

Answer 25

the trapezoid is isosceles. (theo. 6-6-4)

Question 26

A trapezoid is isosceles if and only if its diagonals ….

Answer 26

are congruent. (theo. 6-6-5)

Question 27

TRAPEZOID MIDSEGMENT THEOREM: The midsegment of a trapezoid is …. (a), and its length is …. (b)

Answer 27

(a) parallel to each base

b) one-half the sum of the lengths of the bases. (theo. 6-6-6