Chapter 6

Question 1

Polygon

Answer 1

a plane figure that is formed by three or more segments called sides.

Question 2

consecutive vertices

Answer 2

two vertices that are the endpoints of the same side

Question 3

diagonal

Answer 3

a segment that joins two nonconsecutive vertices of a polygon

Question 4

Types of polygons

Answer 4

triangle, 3 sides
quadrilateral, 4 sides
Pentagon, 5 sides
Hexagon, 6 sides
Heptagon, 7 sides
Octagon, 8 sides

Question 5

Theorem 6.1 “Quadrilateral interior angles theorem”

Answer 5

The sum of the measures of the interior angles of a quadrilateral is 360`

Question 6

parallelogram

Answer 6

a quadrilateral with both pairs of opposite sides parallel.

in ▱ABCD where A-B ll D-C and B-C ll A-D (both sides are congruent)

Question 7

Theorem 6.2 “Quadrilateral parallelogram”

Congruent sides

Answer 7

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

Question 8

Theorem’s 6.3 and 6.4 “Quadrilateral parallelogram” congruent angles and supplementary angles

Answer 8

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

If a quadrilateral is a parallelogram, the its consecutive angles are supplementary

Question 9

Theorem 6.5 “Quadrilateral parallelogram”

diagonals

Answer 9

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

Question 10

Theorem 6.6 “congruent sides converse”

Theorem 6.7 “converse of congruent angles”

Answer 10

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

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

Question 11

Theorem 6.8 “converse of congruent angles”

supplementary

Answer 11

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

Question 12

Theorem 6.9 “converse of diagonals”

Answer 12

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

Question 13

rhombus

Answer 13

a parallelogram with four congruent sides

Question 14

rectangle

Answer 14

a parallelogram with four right angles

Question 15

square

Answer 15

a parallelogram with four congruent sides and four right angles

Question 16

Corollaries

Answer 16

Rhombus Corollary: If a quadrilateral has four congruent sides, then it is a rhombus
Rectangle Corollary: If a quadrilateral has four right angles, then it is a rectangle.
Square corollary: If a quadrilateral has four congruent sides and four right angles, then it is a square.

Question 17

Theorem 6.10 “rhombus diagonals”

Answer 17

The diagonals of a rhombus are perpendicular

Question 18

Theorem 6.11 “rectangle diagonals”

Answer 18

The diagonals of a rectangle are congruent

Question 19

Trapezoid

Answer 19

a quadrilateral with exactly one pair of parallel sides
the parallel sides are the bases
it also has two pairs of base angles and if the legs of a trapezoid are congruent, then the trapezoid is a isosceles trapezoid

Question 20

Theorems 6.12 and 6.13

isosceles

Answer 20

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

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

Question 21

midsegment of a trapezoid

Answer 21

the segment that connects the midpoints of its legs.

mid. = 1/2(sum of the bases lengths