Category 1
What is the definition of a parallelogram?
A quadrilateral in which opposite sides are parallel.
If one base of a trapezoid is 8 and the other base is 10, what is the length of the mid segment?
6
If two pairs of opposite sides are equal, what can be concluded?
The quadrilateral is a parallelogram.
What can be said if both pairs of opposite angles are equal?
The quadrilateral is a parallelogram.
If the are perpendicular to each other, what type of quadrilateral is it?
It is a rhombus!
What is the sum of the interior angles of a parallelogram?
360°
Consider parallelogram ABCD. If the length of side AB is 8, what is the length of the side CD?
8 (because opposite sides are equal).
What are the opposite angles in a parallelogram?
They are equal/congruent.
Consider parallelogram ABCD. If angle A = 70°, what is angle C?
70° (because opposite angles are equal).
Consider parallelogram ABCD. If side AB = 10 and BC = 5, what is the length of CD?
CD=10 (because opposite sides are equal).
What is the definition of a rectangle?
A parallelogram with four right angles.
What defines a rhombus?
A parallelogram with all sides equal.
How is a square different from a rectangle?
A square has all sides equal and all angles are right angles, a rectangle does not have 4 congruent sides.
What theorem or corollary can be used to prove a quadrilateral is a rectangle?
Corollary 7.3/Rectangle Corollary
What properties do trapezoids share with parallelograms?
Trapezoids have one pair of opposite sides (called bases) that are parallel!
What does the Trapezoid Mid segment Theorem state?
The mid segment of a trapezoid is parallel to both bases and its length is the average (or half of the sum) of the lengths of the bases.
What are ALL the conditions (details from theorems!) that would make a quadrilateral a parallelogram?
Opposite sides are equal/congruent, opposite angles are equal/congruent, one set of sides is both parallel and congruent or the diagonals bisect each other.
What is true about the diagonals of an isosceles trapezoid?
They are equal/congruent!
If the legs of a trapezoid are 10 and 14, what is the length of the mid segment?
It is the average of the two bases, so the mid segment = 12!
What is the relationship between the mid segment and the parallel bases?
The mid segment is half the sum of the lengths of the bases.
What is the quadratic formula useful for?
Solving ANY quadratic equation, whether it is factorable or not!
Factor and solve! x2-4 = 0
x=2 x=-2
Factor and solve! x2+18x+81=0
x=-9
What is the quadratic formula?!
x=-b±√b2-4ac/2a
Factor and solve! x2-3x-18=0
x=6 x=-3