Chapter 7 Postulates/Theorems

Question 1

Polygon Interior Angles Theorem

Answer 1

The sum of the measures of the interior angles of a convex n-gon is (n-2) * 180°.

Question 2

Corollary to the Polygon Interior Angles Theorem

Answer 2

The sum of the measures of the interior angles of a quadrilateral is 360°.

Question 3

Polygon Exterior Angles Theorem

Answer 3

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

Question 4

Parallelogram Opposite Sides Theorem

Answer 4

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

Question 5

Parallelogram Opposite Angles Theorem

Answer 5

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

Question 6

Parallelogram Consecutive Angles Theorem

Answer 6

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

Question 7

Parallelogram Diagonals Theorem

Answer 7

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

Question 8

Parallelogram Opposite Sides Converse

Answer 8

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

Question 9

Parallelogram Opposite Angles Converse

Answer 9

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

Question 10

Opposite Sides Parallel and Congruent Theorem

Answer 10

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

Question 11

Parallelogram Diagonals Converse

Answer 11

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

Question 12

Rhombus Corollary

Answer 12

A quadrilateral is a rhombus if and only if it has four congruent sides.

Question 13

Rectangle Corollary

Answer 13

A quadrilateral is a rectangle if and only if it has four right angles.

Question 14

Square Corollary

Answer 14

A quadrilateral is a square if and only if it is a rhombus and a rectangle.

Question 15

Rhombus Diagonals Theorem

Answer 15

A parallelogram is a rhombus if and only if its diagonals are perpendicular.

Question 16

Rhombus Opposite Angles Theorem

Answer 16

A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Question 17

Rectangle Diagonals Theorem

Answer 17

A parallelogram is a rectangle if and only if its diagonals are congruent.

Question 18

Isosceles Trapezoid Base Angles Theorem

Answer 18

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

Question 19

Isosceles Trapezoid Base Angles Converse

Answer 19

If a trapezoid has a pair of congruent base angles, then it is a isosceles trapezoid.

Question 20

Isosceles Trapezoid Diagonals Theorem

Answer 20

A trapezoid is isosceles if and only if its diagonals are congruent.

Question 21

Trapezoid Midsegment Theorem

Answer 21

The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.

Question 22

Kite Diagonals Theorem

Answer 22

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

Question 23

Kite Opposite Angles Theorem

Answer 23

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