Definitions
A quadrilateral with 2 pairs of parallel sides and 2 pairs of congruent sides.
Parallelogram
A trapezoid is a parallelogram.
False
Any rectangle where all sides are congruent.
Square
Diagonals of a parallelogram bisect each other
Midpoint Formula
A quadrilateral ABCD has the following slopes and lengths:
AB: m=4/5; d=3
BC: m=-5/4; d=6
CD: m=4/5; d=3
DA: m=-5/4; d=6
What is the most specific name you can give this quadrilateral?
Rectangle
A quadrilateral with 2 pairs of parallel sides, 4 congruent sides, and 4 right angles.
Square
A rectangle is always a square.
False - not every rectangle has four congruent sides.
One side of a parallelogram is 5 inches and another side is 8 inches. What are the lengths of the other sides?
5 inches and 8 inches
Diagonals of a square are perpendicular
A rectangle ABCD has vertices A(-4,1), B(-3,-3), C(5,-1), and D(4,3).
What is the length of the rectangle's diagonals?
square root of 85
A quadrilateral with 1 pair of parallel sides, 1 pair of congruent sides, and no right angles
Isosceles trapezoid
A square is always a rhombus.
True - Both have 4 congruent sides and 2 pairs of parallel sides.
All shapes that have congruent diagonals.
Square, Rectangle, Isosceles Trapezoid
All sides of a rhombus are equal in length.
Distance Formula
The vertices of quadrilateral ABCD are the following points:
A(-2,2)
B(1,3)
C(2,2)
D(-1,1)
Do the diagonals bisect each other? If they do, what is their common midpoint?
Yes, both diagonals have a midpoint at (0,2).
A quadrilateral with 2 pairs of parallel sides, 2 pairs of congruent sides, and 4 right angles
Rectangle
The rhombus, square, and kite are the only shapes with perpendicular diagonals.
True
All shapes where at least one diagonal bisects the other. Need more than one shape.
Parallelogram, Rectangle, Square, Rhombus, Kite
A trapezoid has one set of parallel sides
Slope formula
The vertices of a quadrilateral are A(-3,1), B(-1,4), C(3,2), and D(1,-2).
What is the most specific name for this shape?
Quadrilateral
A quadrilateral with 2 pairs of parallel sides and 4 congruent sides
Rhombus
A kite can also be a parallelogram.
False - it doesn't have opposite sides that are congruent
Any quadrilateral with opposite sides that are congruent. Need more than one shape.
Parallelogram, Rhombus, Rectangle, Square
A kite has two sets of consecutive congruent sides.
Distance formula
The endpoints of a quadrilateral's diagonals are A(2,1), B(5,5), C(2,9), and D(-1,5).
Based on characteristics of the diagonals, what is the most specific name for this quadrilateral? Why?
It is a rhombus because the diagonals bisect each other, they are perpendicular, and they are NOT congruent.