Coordinate Geometry
If two segments have equal slopes, what does that prove?
They are parallel.
A quadrilateral has one pair of opposite sides that are both parallel and congruent.
Is it a parallelogram?
Yes.
Which shape is always both a rectangle and a rhombus?
Square
What do the diagonals of every parallelogram do?
They bisect each other.
What must be true about the opposite sides of every Parallelogram?
They are parallel and congruent.
f two segments have slopes that are negative reciprocals, what does that prove?
They are perpendicular.
A quadrilateral has diagonals that intersect at their midpoints.
Is it a parallelogram?
Yes. If the diagonals bisect each other, the quadrilateral must be a parallelogram.
Is every rhombus a parallelogram?
Yes
In a rectangle, what is always true about the diagonals?
They are congruent.
If one angle of a parallelogram is 90°, what type of quadrilateral is it?
Rectangle
Points: A(1,2), B(5,2), C(7,6), D(3,6)
What type of quadrilateral is ABCD?
Parallelogram
A quadrilateral has one pair of opposite sides parallel. Is it a parallelogram?
Unknown.
Is every rectangle a rhombus?
No
In a rhombus, what is always true about the diagonals?
They are perpendicular.
A quadrilateral has four congruent sides and opposite angles congruent. What is it?
Rhombus
A quadrilateral has diagonals with the same midpoint. What can you conclude?
It is a parallelogram.
A student says:
“The diagonals are congruent, so the quadrilateral is a parallelogram.”
Is the student correct? If not, what additional information is needed?
No. Congruent diagonals alone do not prove a parallelogram.
Name all 3 quadrilaterals that are always parallelograms.
Rectangle, rhombus, square
Which quadrilateral has diagonals that are both perpendicular and congruent?
Square
A quadrilateral has exactly one pair of parallel sides. What is it?
Trapezoid
Three vertices are A(0,0), B(4,0), C(6,3).
Find the fourth vertex to make a parallelogram.
(2,3)
A quadrilateral has:
Both pairs of opposite sides congruent
All angles are right angles
What is the most specific classification possible?
Rectangle
Which of these is NOT part of the parallelogram family: square, rhombus, kite, rectangle?
Kite
A quadrilateral has perpendicular diagonals, but they do NOT bisect each other. What is the most likely classification?
Kite.
Consecutive angles in a parallelogram always have what relationship?
They are supplementary.