Chapter 6

Front 1

Polygon Angle-Sum Theorem

Back 1

the sum of the measures of the interior angles of and n-gon is (n-2)180

Front 2

Equilateral Polygon

Back 2

a polygon with all sides congruent

Front 3

Equiangular Polygon

Back 3

a polygon with all angles congruent

Front 4

Regular Polygon

Back 4

a polygon that is both equilateral and equiangular

Front 5

Corollary to the Polygon Angle-Sum Theorem

Back 5

the measure of each interior angle of a regular n-gon is (n-2)180 all divided by n

Front 6

Polygon Exterior Angle-Sum Theorem

Back 6

the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360 (360/n)

Front 7

Parallelogram

Back 7

a quadrilateral with both pairs of opposite sides parallel

Front 8

Opposite Sides

Back 8

two sides that do not share a vertex in a quadrilateral

Front 9

Opposite Angles

Back 9

two angles that do not share a side in a quadrilateral

Front 10

Consecutive Angles

Back 10

share a common side in a polygon

Front 11

Theorem 6-3 (opposite sides)

Back 11

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

Front 12

Theorem 6-4 (consecutive angles)

Back 12

if a quadrilateral is a parallelogram, then its consecutive angles are supplementary

Front 13

Theorem 6-5 (opposite angles)

Back 13

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

Front 14

Theorem 6-6 (diagonals)

Back 14

if a quadrilateral is a parallelogram, then its diagonals bisect each other

Front 15

Theorem 6-7 (parallels and transversals)

Back 15

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

Front 16

Theorem 6-8 (opposite sides; parallelogram)

Back 16

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

Front 17

Theorem 6-9 (suppl. consec. <s; parallelogram)

Back 17

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

Front 18

Theorem 6-10 (opp. <s; parallelogram)

Back 18

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

Front 19

Theorem 6-11 (diagonals bisect; parallelogram)

Back 19

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

Front 20

Theorem 6-12 (opp. sides congruent and parallel; parallelogram)

Back 20

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

Front 21

Rhombus

Back 21

parallelogram with four congruent sides

Front 22

Rectangle

Back 22

parallelogram with four right angles

Front 23

Square

Back 23

parallelogram with four congruent sides and four right angles

Front 24

Theorem 6-13 (rhombus diagonals)

Back 24

if parallelogram is a rhombus, then its diagonals are perpendicular

Front 25

Theorem 6-14 (rhombus diagonals bisect opp. <s)

Back 25

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

Front 26

Theorem 6-15 (rectangle diagonals)

Back 26

if a parallelogram is a rectangle, then its diagonals are congruent

Front 27

Theorem 6-16 (diagonals = perpendicular)

Back 27

if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

Front 28

Theorem 6-17 (diagonals; opp. <s)

Back 28

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

Front 29

Theorem 6-18 (congruent diagonals)

Back 29

if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

Front 30

trapezoid

Back 30

quadrilateral with exactly one pair of parallel sides

Front 31

bases of a trapezoid

Back 31

parallel sides of a trapezoid

Front 32

legs of a trapezoid

Back 32

nonparallel sides of a trapezoid

Front 33

base angles of a trapezoid

Back 33

two angles that share a base of a trapezoid

Front 34

isosceles trapezoid

Back 34

trapezoid with legs that are congruent

Front 35

Theorem 6-19 (isosceles trapezoid)

Back 35

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

Front 36

Theorem 6-20 (isos. trap. diagonals)

Back 36

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

Front 37

midsegment of a trapezoid

Back 37

segment that joins the midpoints of the legs of a trapezoid

Front 38

Trapezoid Midsegment Theorem

Back 38

if a quadrilateral is a trapezoid, then the midsegment is parallel to the bases, and the length of the midsegment is half the sum of the lengths of the bases

Front 39

kite

Back 39

quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent

Front 40

Theorem 6-22 (kite diagonals)

Back 40

if a quadrilateral is a kite, then its diagonals are perpendicular

Front 41

Distance Formula

Back 41

to determine whether sides are congruent and diagonals are congruent

Front 42

Midpoint Formula

Back 42

to determine the coordinates of the midpoint of a side and whether diagonals bisect each other

Front 43

Slope Formula

Back 43

the determine whether opposite sides are parallel, diagonals are perpendicular, and sides are perpendicular

Front 44

coordinate proof

Back 44

using coordinate geometry and algebra to prove theorems