Chapter 6 Overview Flashcards

1
Q

Theorem 6-1: Polygon Angle-Sum Theorem

A

The sum of the measures of the interior angles of an n-gon is (n-2)180.

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2
Q

Equilateral Polygon

A

all sides are congruent

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3
Q

Equiangular Polygon

A

all angles in the interior of a polygon are congruent

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4
Q

Regular Polygon

A

a convex polygon that is both equiangular and equilateral

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5
Q

Corollary to the Polygon Angle-Sum Theorem

A

The measure of each interior angle of a regular n-gon is (n-2)180/n

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6
Q

Theorem 6-2: Polygon Exterior Angle-Sum Theorem

A

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

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7
Q

parallelogram

A

quadrilateral with both pairs of opposite sides parallel

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8
Q

opposite sides of a parallelogram

A

the do not share a vertex

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9
Q

Theorem 6-4

A

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

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10
Q

Theorem 6-3

A

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

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11
Q

Theorem 6-5

A

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

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12
Q

Theorem 6-6

A

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

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13
Q

Theorem 6-7

A
If 3(or more) parallel lines cut off congruent segments in one transversal, then
they cut off congruent segments on every transversal.
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14
Q

Theorem 6-8

A

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

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15
Q

Theorem 6-9

A

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

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16
Q

Theorem 6-10

A

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

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17
Q

Theorem 6-11

A

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

18
Q

Theorem 6-12

A

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

19
Q

rhombus

A

a parallelogram with 4 congruent sides

20
Q

rectangle

A

a parallelogram with 4 right angles

21
Q

square

A

a parallelogram with 4 congruent sides and 4 right angles

22
Q

Theorem 6-13

A

If a parallelogram is a rhombus, then its diagonals are ⊥.

23
Q

Theorem 6-14

A

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

24
Q

Theorem 6-15

A

If a parallelogram is a rectangle, then its diagonals are ≅.

25
**Every square is both a rhombus and rectangle. A square must have all the properties of parallelograms, rhombuses, and rectangles.
**Every square is both a rhombus and rectangle. A square must have all the properties of parallelograms, rhombuses, and rectangles.
26
Theorem 3-16
If the diagonals of a parallelogram are ⊥, then the parallelogram is a rhombus.
27
*You can determine whether a parallelogram is a rhombus or a rectangle based on the properties of its diagonals.
*If a parallelogram is both a rectangle and a rhombus, then it is a square.
28
Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.
29
Theorem 6-18
If the diagonals of a parallelogram are ≅, then the parallelogram is a rectangle.
30
trapezoid
quadrilateral with exactly one pair of parallel sides bases – parallel sides of trapezoid legs – 2 nonparallel sides of trapezoid
31
isosceles trapezoid
trapezoid with legs that are ≅
32
Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.
33
Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.
34
midsegment of a trapezoid
the segment that joins the midpoints of a | trapezoid’s legs
35
Theorem 6-21 Trapezoid Midsegment Theorem
If a quadrilateral is a trapezoid, then (1) the segment is ∥ to the bases, and (2) the length of the midsegment is half the sum of the lengths of the bases.
36
kite
quadrilateral with 2 pairs of consecutive sides ≅ and no opposite sides ≅
37
Theorem 6-22
If a quadrilateral is a kite, then its diagonals are ⊥.
38
Distance Formula and When to Use
d = (x2 − x1) ^2 + (y2 − y1) ^2 To determine whether - sides are ≅ - diagonals are ≅
39
Midpoint Formula and When to Use
x1+x2 y1+y2 m = ---------- , ------------ 2 2 - the coordinates of the midpt of a side - whether diagonals bisect each other
40
Slope Formula and When to Use
y2−y1 m = ----------- x2−x1 - opposite sides are ∥ - diagonals are ⊥ - sides are ⊥
41
You can use variables to name the coordinates of a figure. This allows you to show that relationships are true for a general case.
You can use variables to name the coordinates of a figure. This allows you to show that relationships are true for a general case.