Why is it that the statement "all rhombuses are squares" is false, but the statement "all squares are rhombuses" is true? Use an example to help with your explanation.
Given two segments with lengths x and y (x does not equal y), which three special parallelograms meets each set of given conditions?
Parallelogram where one diagonal has length x, the other has length y.
Parallelogram where the diagonals intersect at right angles.
Parallelogram where both diagonals have length y and do not intersect at right angles.
The diagonals of a parallelogram are 2.3cm and 3.2cm long. Can you tell if the parallelogram is a rhombus? Explain how you know.
What type of quadrilateral is formed by connecting the points (0,9), (3,6), (0,1), and (-3,6)? Explain how you know.
What type of quadrilateral is formed by connecting the points (0,0), (3x,b), (18x,b), and (15x,0)? Explain how you know.(If you need to, replace variable-x with an integer before sketching the figure.)
How would you use coordinate geometry to prove that two line segments are perpendicular? Provide an example to help with your explanation.