Chapter 6

Question 0

Polygon

Answer 0

A plane figure formed by three or more segments called sides such that:

1. ) each side intersects exactly two other sides, once at each endpoint.
2. ) No two sides with a common endpoint are collinear.

Question 1

Convex Polgon

Answer 1

A polygon such that no line that contains a side of a polygon contains a point in the interior of the polygon.

Question 2

Concave Polygon

Answer 2

Polygon that is not convex

Question 3

Diagonal of a Polygon

Answer 3

A segment that joins two nonconsecutive vertices.

Question 4

Equilateral

Answer 4

All sides congruent

Question 5

Equiangular

Answer 5

All angles congruent

Question 6

Polygon Interior Angle Theorem

Answer 6

The sum of the interior angles of a convex n-gon (n-2)180

Question 7

Corollary to Polygon Interior Angle Theorem

Answer 7

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

Question 8

Polygon Exterior Angles Theorem

Answer 8

The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360

Question 9

Corollary to Polygon Exterior Angles Theorem

Answer 9

The measure of each exterior angle in a regular n-gon 360/n

Question 10

Regular Polygon

Answer 10

All sides and angles congruent

Question 11

Parallelogram

Answer 11

A quadrilateral whose opposite sides are parallel.

Question 12

Theorem 6.3

Answer 12

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

Question 13

Theorem 6.4

Answer 13

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

Question 14

Theorem 6.5

Answer 14

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

Question 15

Diagonals of a Parallelogram Theorem

Answer 15

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

Question 16

Theorem 6.7

Answer 16

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

Question 17

Theorem 6.8

Answer 17

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

Question 18

Theorem 6.9

Answer 18

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

Question 19

Theorem 6.10

Answer 19

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

Question 20

Theorem 6.11

Answer 20

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

Question 21

Rhombus

Answer 21

Parallelogram with 4 congruent sides.

Question 22

Rectangle

Answer 22

Parallelogram with 4 right angles.

Question 23

Square

Answer 23

Parallelogram with 4 congruent sides and 4 right angles. (Both a rhombus and rectangle.)

Question 24

Theorem 6.12

Answer 24

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

Question 25

Theorem 6.13

Answer 25

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

Question 26

Theorem 6.14

Answer 26

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

Question 27

Theorem 6.15

Answer 27

A quadrilateral is a rhombus if and only if it has 4 congruent sides

Question 29

Theorem 6.16

Answer 29

A quadrilateral is a rectangle if and only if it has 4 right angles.

Question 30

Trapezoid

Answer 30

Quadrilateral with exactly one pair of parallel sides.

Question 31

Base

Answer 31

Parallel sides

Question 32

Legs

Answer 32

non-parallel sides

Question 33

Base Angles

Answer 33

Pair of angles that share a common base.

each trapezoid has two pairs

Question 34

Isosceles Trapezoid

Answer 34

Trapezoid with congruent legs.

Question 35

Trapezoid Base Angles Theorem

Answer 35

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

Question 36

Trapezoid Diagonals Theorem

Answer 36

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

Question 37

Theorem 6.19

Answer 37

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

Question 38

Theorem 6.20

Answer 38

If a trapezoid has congruent diagonals, then the trapezoid is isosceles.

Question 39

Midsegment of A Trapezoid

Answer 39

Segment that connects the midpoints of the legs.

Question 40

Trapezoid Midsegment Theorem

Answer 40

The midsegment of a trapezoid is:

1. ) Parallel to each base
2. ) Its length is 1/2 the sum of the length of the bases.