Chapter 6 Flashcards

1
Q

Polygon

A

A closed planed figure formed by 3 or more segments

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2
Q

Triangle

A

3 sided

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3
Q

Quadrilateral

A

4 sided

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4
Q

Pentagon

A

5 sided

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5
Q

Hexagon

A

6 sided

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6
Q

Septagon/Heptagon

A

7 sided

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7
Q

Octogon

A

8 sided

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8
Q

Nonagon

A

9 sided

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9
Q

Decagon

A

10 sided

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10
Q

Hendecagon

A

11 sided

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11
Q

Dodecagon

A

12 sided

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12
Q

n-gon

A

n sides

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13
Q

Regular Polygon

A

Both equilateral and equiangular

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14
Q

Concave

A

Diagonals on exterior

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15
Q

Convex

A

Diagonals in interior

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16
Q

Polygon Angle Sum Theorem

A

The sum of the interior angle measures of a convex polygon with n sides is:

(n-2)180

17
Q

Polygon Exterior Angle Sum Theorem

A

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

18
Q

Parallelogram

A

A quadrilateral with 2 pairs of parallel sides

19
Q

Parallelogram Theorems

A
  • If a quadrilateral is a parallelogram, then its opposite angles are congruent
  • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary
  • If a quadrilateral is a parallelogram, then its diagonals bisect each other
  • If a quadrilateral is a parallelogram, then its opposite sides are congruent
20
Q

Conditions for Parallelograms

A
  • Both pairs of opposite sides are parallel
  • One pair of opposite sides are parallel and congruent
  • Both pairs of opposite sides are congruent
  • Both pairs of opposite angles are congruent
  • One angle is supplementary to both of its consecutive angles
  • The diagonals bisect each other
21
Q

Rectangle

A

A quadrilateral with 4 right angles

22
Q

Properties of Rectangles

A
  • If a quadrilateral is a rectangle, then it is a parallelogram
  • If a parallelogram is a rectangle, then its diagonals are congruent
23
Q

Rhombus

A

A quadrilateral with 4 congruent sides

24
Q

Properties of Rhombi

A
  • If a quadrilateral is a rhombus, then it is a parallelogram (rhombus –> parallelogram)
  • If a parallelogram is a rhombus, then its diagonals are perpendicular (rhombus –> perpendicular diags.)
  • If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles (rhombus –> each diagonal bisects opposite angles)
25
Q

Square

A

A quadrilateral with 4 congruent sides and 4 right angles

26
Q

Properties of Squares

A
  • Square is a parallelogram
  • Square is a rectangle
  • Square is a rhombus

*Properties apply for all 3

27
Q

Conditions for Rectangles

A
  • If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle
  • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
28
Q

Conditions for Rhombuses

A
  • If one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus
  • If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
  • If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus
29
Q

Kite

A

A quadrilateral with exactly 2 pairs of congruent consecutive sides

30
Q

Properties of a Kite

A
  • If a quadrilateral is a kite, then its diagonals are perpendicular
  • If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
  • Kite –> one diagonal bisects opposite angles
31
Q

Trapezoid

A

Quadrilateral with one pair of parallel sides

32
Q

Isosceles Trapezoid

A

Trapezoid with congruent legs

33
Q

Properties of Isosceles Trapezoids

A
  • If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent
  • If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles
  • A trapezoid is an
    isosceles if and only if its diagonals are congruent
34
Q

Mid-segment of a Trapezoid

A

A segment whose endpoints are the midpoints of the legs

35
Q

Trapezoid Mid-segment Theorem

A

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