Chapter 7 Big ideas math geometry

studied byStudied by 9 people
0.0(0)
Get a hint
Hint

Diagonal

1 / 43

flashcard set

Earn XP

Description and Tags

44 Terms

1

Diagonal

a segment that connects any two nonconsecutive vertices

<p>a segment that connects any two nonconsecutive vertices</p>
New cards
2

Polygon Interior Angles Theorem

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

<p>The sum of the measures of the interior angles of a convex n-gon is (n-2)*180</p>
New cards
3

Corollary to the Polygon Interior Angles Theorem

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

<p>The sum of the measures of the interior angles of a quadrilateral is 360 degrees</p>
New cards
4

equilateral polygon

a polygon with all sides congruent

<p>a polygon with all sides congruent</p>
New cards
5

equiangular polygon

a polygon in which all angles are congruent

<p>a polygon in which all angles are congruent</p>
New cards
6

regular polygon

a convex polygon that is both equilateral and equiangular

<p>a convex polygon that is both equilateral and equiangular</p>
New cards
7

Polygon exterior angles theorem

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

<p>The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360Ā°</p>
New cards
8

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

<p>a quadrilateral with both pairs of opposite sides parallel</p>
New cards
9

Parallelogram opposite sides theorem

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

<p>If a quadrilateral is a parallelogram, then its opposite sides are congruent.</p>
New cards
10

Parallelogram opposite angles theorem

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

<p>If a quadrilateral is a parallelogram, then its opposite angles are congruent.</p>
New cards
11

Parallelogram Consecutive Angles Theorem

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

<p>If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.</p>
New cards
12

Parallelogram Diagonals Theorem

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

<p>If a quadrilateral is a parallelogram, then its diagonals bisect each other.</p>
New cards
13

Parallelogram opposite sides converse

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

<p>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram</p>
New cards
14

Parallelogram opposite angles converse

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

<p>If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram</p>
New cards
15

Opposite sides parallel and congruent theorem

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

<p>If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.</p>
New cards
16

Parallelogram diagonals converse

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

<p>If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.</p>
New cards
17

quadrilateral

a four-sided polygon

New cards
18

Pentagon

5 sided polygon

New cards
19

Hexagon

6 sides

New cards
20

heptagon/septagon

a polygon with 7 sides

New cards
21

Octagon

a polygon with 8 sides

New cards
22

nonagon

polygon with 9 sides

New cards
23

decagon

a polygon with 10 sides

New cards
24

Hendecagon

11 sided polygon

New cards
25

Dodecagon

12 sided polygon

New cards
26

Rhombus

A parallelogram with four congruent sides

New cards
27

rectangle

A parallelogram with four right angles

New cards
28

Square

A parallelogram with four congruent sides and four right angles.

New cards
29

Rhombus Corollary

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

New cards
30

Rectangle Corollary

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

New cards
31

Square Corollary

A quadrilateral is a square if and only if it is a rhombus and a rectangle.

New cards
32

Rhombus Diagonals Theorem

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

New cards
33

Rhombus Opposite Angles Theorem

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

New cards
34

Rectangle Diagonals Theorem

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

New cards
35

Trapezoid

A quadrilateral with exactly one pair of parallel sides

New cards
36

Isosceles trapezoid

a trapezoid in which the legs are congruent

New cards
37

Isosceles trapezoid base angles theorem

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

New cards
38

Isosceles trapezoid base angles converse

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

New cards
39

Isosceles trapezoid diagonals theorem

A trapezoid is isosceles if and only if its diagonals are congruent.

New cards
40

midsegment of a trapezoid

a segment that connects the midpoints of the legs of a trapezoid

New cards
41

Trapezoid Midsegment Theorem

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

New cards
42

Kite

a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

New cards
43

Kite Diagonals Theorem

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

New cards
44

Kite Opposite Angles Theorem

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

New cards

Explore top notes

note Note
studied byStudied by 57 people
... ago
5.0(1)
note Note
studied byStudied by 17 people
... ago
5.0(1)
note Note
studied byStudied by 31 people
... ago
5.0(2)
note Note
studied byStudied by 440 people
... ago
5.0(2)
note Note
studied byStudied by 28 people
... ago
5.0(2)
note Note
studied byStudied by 17 people
... ago
5.0(1)
note Note
studied byStudied by 19 people
... ago
5.0(1)
note Note
studied byStudied by 8 people
... ago
5.0(1)

Explore top flashcards

flashcards Flashcard (20)
studied byStudied by 5 people
... ago
5.0(1)
flashcards Flashcard (64)
studied byStudied by 80 people
... ago
5.0(5)
flashcards Flashcard (22)
studied byStudied by 33 people
... ago
5.0(2)
flashcards Flashcard (22)
studied byStudied by 70 people
... ago
5.0(2)
flashcards Flashcard (177)
studied byStudied by 7 people
... ago
5.0(2)
flashcards Flashcard (116)
studied byStudied by 7 people
... ago
5.0(1)
flashcards Flashcard (36)
studied byStudied by 3 people
... ago
5.0(1)
flashcards Flashcard (125)
studied byStudied by 30 people
... ago
5.0(1)
robot