Chapter 6

Question 1

What is a parallelogram?

Answer 1

a quadrilateral with both pairs of opposite sides parallel

Question 2

Properties of Parallelograms (hint: there are 4)

Answer 2

1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supplementary

Question 3

6-4 (parallel lines and transversals)

Answer 3

If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

Question 4

Distance Formula:

Answer 4

d = square root of (x2-x1) squared + (y2-y1) squared

Question 5

Midpoint Formula:

Answer 5

m = (x1 + x2 / 2 , y1 + y2 / 2)

Question 6

Slope Formula:

Answer 6

m = y2 - y1 / x2 - x1

OR

run

Question 7

6-5 (opposite sides)

Answer 7

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

Question 8

6-6 (opposite angles)

Answer 8

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

Question 9

6-7 (diagonals)

Answer 9

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

Question 10

6-8 (one pair)

Answer 10

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

Question 11

5 ways to prove a quadrilateral is a parallelogram

Answer 11

1. Both pairs of opposite sides are parallel (def of parallelogram)
2. Both pairs of opposite sides are congruent
3. Both pairs of opposite angles are congruent
4. The diagonals bisect each other (have the same midpoint)
5. One pair of opposite sides is parallel and congruent

Question 12

def of rhombus

Answer 12

a parallelogram with 2 congruent, consecutive sides

Question 13

6-9 (diagonal —> angles; rhombus)

Answer 13

Each diagonal of a rhombus bisects 2 angles of a rhombus

Question 14

6-10 (rhombus diagonals)

Answer 14

The diagonals of a rhombus are perpendicular

Question 15

def of rectangle

Answer 15

parallelogram with 1 right angle

Question 16

6-11 (rectangle diagonals)

Answer 16

The diagonals of a rectangle are congruent

Question 17

def of square

Answer 17

a rectangle and a rhombus

Question 18

what is special about a square

Answer 18

has properties of a parallelogram, rhombus, and rectangle

Question 19

what is special about the DIAGONALS of a square

Answer 19

they are:

• congruent
• bisect each other
• each bisect two angles
• and are perpendicular

Question 20

6-12 and 6-13 (proving a parallelogram is a rhombus)

Answer 20

6-12 : If one diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus

6-13 : If the diagonals of a parallelogram are perpendicular, then it is a rhombus

Question 21

6-14 (proving a parallelogram is a rectangle)

Answer 21

If the diagonals of a parallelogram are congruent, then it is a rectangle

Question 22

def of trapezoid

Answer 22

quad with one pair of parallel sides

Question 23

what sides of a trapezoid are the bases?

Answer 23

the parallel sides

Question 24

what sides of a trapezoid are the legs?

Answer 24

the nonparallel sides

Question 25

what are the base angles?

Answer 25

angles that share a base

Question 26

what is special about isosceles trapezoids

Answer 26

legs are congruent

Question 27

what is special about 2 angles that share a leg?

Answer 27

they are supplementary

Question 28

6-15 (base angles of isosceles trapezoid)

Answer 28

base angles are congruent

Question 29

6-16 (diagonals of isosceles trapezoid)

Answer 29

diagonals are congruent

Question 30

def of kite

Answer 30

2 pairs consecutive/adjacent congruent sides

Question 31

6-17 (kite diagonals)

Answer 31

the diagonals of a kite are perpendicular

Question 32

Trapezoid Midsegment Theorem

Answer 32

The midsegment of a trapezoid is parallel to the bases and the length of the midsegment is HALF THE SUM OF THE LENGTHS OF THE BASES

Question 33

when figuring out which answer to use after factoring, remember…

Answer 33

YOU CANNOT HAVE A NEGATIVE SIDE