Chapter 6 Overview

Question 1

Theorem 6-1: Polygon Angle-Sum Theorem

Answer 1

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

Question 2

Equilateral Polygon

Answer 2

all sides are congruent

Question 3

Equiangular Polygon

Answer 3

all angles in the interior of a polygon are congruent

Question 4

Regular Polygon

Answer 4

a convex polygon that is both equiangular and equilateral

Question 5

Corollary to the Polygon Angle-Sum Theorem

Answer 5

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

Question 6

Theorem 6-2: Polygon Exterior Angle-Sum Theorem

Answer 6

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

Question 7

parallelogram

Answer 7

quadrilateral with both pairs of opposite sides parallel

Question 8

opposite sides of a parallelogram

Answer 8

the do not share a vertex

Question 9

Theorem 6-4

Answer 9

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

Question 10

Theorem 6-3

Answer 10

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

Question 11

Theorem 6-5

Answer 11

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

Question 12

Theorem 6-6

Answer 12

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

Question 13

Theorem 6-7

Answer 13

If 3(or more) parallel lines cut off congruent segments in one transversal, then
they cut off congruent segments on every transversal.

Question 14

Theorem 6-8

Answer 14

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

Question 15

Theorem 6-9

Answer 15

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

Question 16

Theorem 6-10

Answer 16

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

Question 17

Theorem 6-11

Answer 17

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

Question 18

Theorem 6-12

Answer 18

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

Question 19

rhombus

Answer 19

a parallelogram with 4 congruent sides

Question 20

rectangle

Answer 20

a parallelogram with 4 right angles

Question 21

square

Answer 21

a parallelogram with 4 congruent sides and 4 right angles

Question 22

Theorem 6-13

Answer 22

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

Question 23

Theorem 6-14

Answer 23

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

Question 24

Theorem 6-15

Answer 24

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

Question 25

**Every square is both a rhombus and
rectangle. A square must have all the
properties of parallelograms, rhombuses,
and rectangles.

Answer 25

**Every square is both a rhombus and
rectangle. A square must have all the
properties of parallelograms, rhombuses,
and rectangles.

Question 26

Theorem 3-16

Answer 26

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

Question 27

*You can determine whether a parallelogram is a rhombus or a rectangle based
on the properties of its diagonals.

Answer 27

*If a parallelogram is both a rectangle and a rhombus, then it is a square.

Question 28

Theorem 6-17

Answer 28

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

Question 29

Theorem 6-18

Answer 29

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

Question 30

trapezoid

Answer 30

quadrilateral with exactly one pair of parallel sides

bases – parallel sides of trapezoid
legs – 2 nonparallel sides of trapezoid

Question 31

isosceles trapezoid

Answer 31

trapezoid with legs that are ≅

Question 32

Theorem 6-19

Answer 32

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

Question 33

Theorem 6-20

Answer 33

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

Question 34

midsegment of a trapezoid

Answer 34

the segment that joins the midpoints of a

trapezoid’s legs

Question 35

Theorem 6-21 Trapezoid Midsegment Theorem

Answer 35

If a quadrilateral is a trapezoid, then (1) the segment is ∥ to the bases, and (2)
the length of the midsegment is half the sum of the lengths of the bases.

Question 36

kite

Answer 36

quadrilateral with 2 pairs of consecutive sides ≅ and no opposite sides ≅

Question 37

Theorem 6-22

Answer 37

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

Question 38

Distance Formula and When to Use

Answer 38

d = (x2 − x1) ^2 + (y2 − y1) ^2

To determine whether

• sides are ≅
• diagonals are ≅

Question 39

Midpoint Formula and When to Use

Answer 39

x1+x2 y1+y2
m = ———- , ————
2 2

• the coordinates of the midpt of
  a side
• whether diagonals bisect each other

Question 40

Slope Formula and When to Use

Answer 40

y2−y1
m = ———–
x2−x1

• opposite sides are ∥
• diagonals are ⊥
• sides are ⊥

Question 41

You can use variables to name the coordinates of a figure. This allows you to
show that relationships are true for a general case.

Answer 41

You can use variables to name the coordinates of a figure. This allows you to
show that relationships are true for a general case.