Chapter 6 Flashcards
What is a parallelogram?
a quadrilateral with both pairs of opposite sides parallel
Properties of Parallelograms (hint: there are 4)
- Opposite sides are congruent
- Opposite angles are congruent
- Diagonals bisect each other
- Consecutive angles are supplementary
6-4 (parallel lines and transversals)
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
Distance Formula:
d = square root of (x2-x1) squared + (y2-y1) squared
Midpoint Formula:
m = (x1 + x2 / 2 , y1 + y2 / 2)
Slope Formula:
m = y2 - y1 / x2 - x1
OR
run
6-5 (opposite sides)
If both pairs of opposite sides of a quad are congruent, then the quad is a parallelogram
6-6 (opposite angles)
If both pairs of opposite angles of a quad are congruent, then the quad is a parallelogram
6-7 (diagonals)
If the diagonals of a quad bisect each other, then the quad is a parallelogram
6-8 (one pair)
If one pair off opposite sides of a quad is both congruent and parallel, then the quad is a parallelogram
5 ways to prove a quadrilateral is a parallelogram
- Both pairs of opposite sides are parallel (def of parallelogram)
- Both pairs of opposite sides are congruent
- Both pairs of opposite angles are congruent
- The diagonals bisect each other (have the same midpoint)
- One pair of opposite sides is parallel and congruent
def of rhombus
a parallelogram with 2 congruent, consecutive sides
6-9 (diagonal —> angles; rhombus)
Each diagonal of a rhombus bisects 2 angles of a rhombus
6-10 (rhombus diagonals)
The diagonals of a rhombus are perpendicular
def of rectangle
parallelogram with 1 right angle
6-11 (rectangle diagonals)
The diagonals of a rectangle are congruent
def of square
a rectangle and a rhombus
what is special about a square
has properties of a parallelogram, rhombus, and rectangle
what is special about the DIAGONALS of a square
they are:
- congruent
- bisect each other
- each bisect two angles
- and are perpendicular
6-12 and 6-13 (proving a parallelogram is a rhombus)
6-12 : If one diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus
6-13 : If the diagonals of a parallelogram are perpendicular, then it is a rhombus
6-14 (proving a parallelogram is a rectangle)
If the diagonals of a parallelogram are congruent, then it is a rectangle
def of trapezoid
quad with one pair of parallel sides
what sides of a trapezoid are the bases?
the parallel sides
what sides of a trapezoid are the legs?
the nonparallel sides
what are the base angles?
angles that share a base
what is special about isosceles trapezoids
legs are congruent
what is special about 2 angles that share a leg?
they are supplementary
6-15 (base angles of isosceles trapezoid)
base angles are congruent
6-16 (diagonals of isosceles trapezoid)
diagonals are congruent
def of kite
2 pairs consecutive/adjacent congruent sides
6-17 (kite diagonals)
the diagonals of a kite are perpendicular
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to the bases and the length of the midsegment is HALF THE SUM OF THE LENGTHS OF THE BASES
when figuring out which answer to use after factoring, remember…
YOU CANNOT HAVE A NEGATIVE SIDE
