Chapter 6 Overview Flashcards
Theorem 6-1: Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is (n-2)180.
Equilateral Polygon
all sides are congruent
Equiangular Polygon
all angles in the interior of a polygon are congruent
Regular Polygon
a convex polygon that is both equiangular and equilateral
Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is (n-2)180/n
Theorem 6-2: Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360
parallelogram
quadrilateral with both pairs of opposite sides parallel
opposite sides of a parallelogram
the do not share a vertex
Theorem 6-4
If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary.
Theorem 6-3
If a quadrilateral is a parallelogram, then its opposite sides are congruent
Theorem 6-5
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Theorem 6-6
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6-7
If 3(or more) parallel lines cut off congruent segments in one transversal, then they cut off congruent segments on every transversal.
Theorem 6-8
If both pairs of opposite sides of a quadrilateral are ≅, then the quadrilateral is a
parallelogram.
Theorem 6-9
If an angle of a quadrilateral is supplementary to both of its consecutive angles,
then the quadrilateral is a parallelogram.
Theorem 6-10
If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6-11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a
parallelogram.
Theorem 6-12
If one pair of opposite sides of a quadrilateral is both congruent and parallel,
then the quadrilateral is a parallelogram.
rhombus
a parallelogram with 4 congruent sides
rectangle
a parallelogram with 4 right angles
square
a parallelogram with 4 congruent sides and 4 right angles
Theorem 6-13
If a parallelogram is a rhombus, then its diagonals are ⊥.
Theorem 6-14
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite
angles.
Theorem 6-15
If a parallelogram is a rectangle, then its diagonals are ≅.
**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.
Theorem 3-16
If the diagonals of a parallelogram are ⊥, then the parallelogram is a rhombus.
*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.
Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the
parallelogram is a rhombus.
Theorem 6-18
If the diagonals of a parallelogram are ≅, then the parallelogram is a rectangle.
trapezoid
quadrilateral with exactly one pair of parallel sides
bases – parallel sides of trapezoid
legs – 2 nonparallel sides of trapezoid
isosceles trapezoid
trapezoid with legs that are ≅
Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is
congruent.
Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.
midsegment of a trapezoid
the segment that joins the midpoints of a
trapezoid’s legs
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.
kite
quadrilateral with 2 pairs of consecutive sides ≅ and no opposite sides ≅
Theorem 6-22
If a quadrilateral is a kite, then its diagonals are ⊥.
Distance Formula and When to Use
d = (x2 − x1) ^2 + (y2 − y1) ^2
To determine whether
- sides are ≅
- diagonals are ≅
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
Slope Formula and When to Use
y2−y1
m = ———–
x2−x1
- opposite sides are ∥
- diagonals are ⊥
- sides are ⊥
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.
