1) Imagine a figure that is a parallelogram. Give the figure another property that would then make the figure also a rectangle. Give two separate examples.
6) Figure \(MNPQ\) has vertices \(M(-1, 5)\), \(N(1, 2)\), \(P(-2, 0)\), and \(Q(-4, 3)\). What is its most descriptive name?
9) Answer True or False:
a) To prove a quadrilateral is a rectangle, prove it is equilateral.
b) To prove a trapezoid is isosceles, prove its base angles are congruent.
c) To prove a parallelogram is a rectangle, prove its diagonals are perpendicular.
d) To prove a rectangle is a square, prove that it also has four congruent sides.
e) To prove a rhombus is a square, prove that it also has congruent diagonals.
f) To prove a quadrilateral is an isosceles trapezoid, prove it has exactly one pair of opposite sides parallel and its
diagonals are congruent.
g) To prove a parallelogram is a rhombus, prove that its diagonals bisect its interior angles.
h) To prove a quadrilateral is a kite, prove that its diagonals are perpendicular bisectors of each other.
i) To prove a parallelogram is a square, prove that its diagonals are perpendicular.
j) To prove a quadrilateral is a kite, prove diagonals are perpendicular but only one diagonal bisects the other.
k) To prove a quadrilateral is a rhombus, prove it is equiangular.
l) To prove a quadrilateral is a rectangle, show that all of its adjacent sides have slopes that are opposite reciprocals of
each other.
m) To prove a quadrilateral is a kite, tie a tail on it and see if it flies.
a) To prove a quadrilateral is a rectangle, prove it is equilateral.
b) To prove a trapezoid is isosceles, prove its base angles are congruent.
c) To prove a parallelogram is a rectangle, prove its diagonals are perpendicular.
d) To prove a rectangle is a square, prove that it also has four congruent sides.
e) To prove a rhombus is a square, prove that it also has congruent diagonals.
f) To prove a quadrilateral is an isosceles trapezoid, prove it has exactly one pair of opposite sides parallel and its
diagonals are congruent.
g) To prove a parallelogram is a rhombus, prove that its diagonals bisect its interior angles.
h) To prove a quadrilateral is a kite, prove that its diagonals are perpendicular bisectors of each other.
i) To prove a parallelogram is a square, prove that its diagonals are perpendicular.
j) To prove a quadrilateral is a kite, prove diagonals are perpendicular but only one diagonal bisects the other.
k) To prove a quadrilateral is a rhombus, prove it is equiangular.
l) To prove a quadrilateral is a rectangle, show that all of its adjacent sides have slopes that are opposite reciprocals of
each other.
m) To prove a quadrilateral is a kite, tie a tail on it and see if it flies.
11) Given the following diagrams as marked, give the most descriptive name for each figure. NOTE: the figures are NOT drawn to scale.
12) Name as many ways possible one could prove a figure is a square. NOTE: there are many more than two.
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