Show:
Parallelograms
Rhombuses
Rectangles
Squares
Miscellaneous
100
Name a property that the diagonals of a parallelogram have.
The diagonals bisect each other.
100
In Rhombus MNOP, MN = 24, and NO = 2x + 6. What is the value of x?
x = 9, because consecutive sides of a rhombus are congruent, so MN = NO.
100
Name the 2 properties that the diagonals of a rectangle have.
They are congruent and bisect each other.
100
How do you prove a rectangle is a square?
Show it has 2 congruent adjacent sides. Also acceptable, show all 4 sides are congruent.
100
In a trapezoid, the upper base is 12, and the lower base is 30. What is the median of the trapezoid?
1/2(12 + 30 ) = 1/2(42) = 21
200
If ABCD is a parallelogram and angle A = 2x + 40, and angle B = 3x - 10. Explain how you would set up the equation.
Add the expressions and set them equal to 180 degrees. ( Consecutive Angles are Supplementary )
200
Can a rhombus be a rectangle? If so, draw a picture. If not, explain why not.
Yes, it would look like a square. It has all the properties of a rhombus and rectangle.
200
In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x?
x = 5. The diagonals are congruent so AC = BD.
200
How do you prove a rhombus is a square?
Show it has ONE right angle. Also accpetable, Show it has 4 right angles.
200
A quadrilateral has the following properties: Its diagonals bisect the angles. Its diagonals are not congruent. Choose any of the following that it could be. I.) isosceles trapezoid II.) rhombus III.) rectangle IV.) parallelogram V.) square
II.) rhombus only
300
If ABCD is a parallelogram, and AB = 3x - 5, and BC = 6x - 2, and AD = 2x + 12. Explain the equation used to solve the problem.
Set the expressions for sides BC and AD equal to one another. Opposite sides of a parallelogram are congruent.
300
In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72, what is the measure of angle CBD?
Angle CBD = 54, use the right triangles formed by the diagonals, and the fact that the angles bisect the corner angles.
300
In rectangle ABCD, the diagonals intersect at E. AE = 4x + 20, BC = 7x + 12 and DE = 8x + 4. What is the value of x?
x = 4. The diagonals bisect each other and are congruent, so AE = DE.
300
Name at least 7 properties of a square.
(DIAGONALS): perpendicular, congruent, bisect each other, bisect the angles (SIDES): all 4 sides are congruent, opposite sides parallel ( ANGLES): All 4 angles are congruent, consecutive angles are supplementary.
300
In an isosceles trapezoid, which of the following are NOT true? Choose all that apply. I.) the diagonals bisect each other II.) the diagonals are congruent III.) the upper base angles are congruent IV.) the non parallel sides are congruent
I only.
400
To prove a quadrilateral is a parallelogram, show which of the following: ( You may choose more than one. ) I.) Both pairs of opposite sides are congruent. II.) Both pairs of opposite sides are parallel. III.) One pair of sides are parallel and congruent. IV.) The diagonals are congruent.
I, II, and III only. The diagonals are not congruent, they BISECT EACH OTHER.
400
Name the 3 properties that the diagonals of a rhombus have.
diagonals bisect each other, diagonals are perpendicular, diagonals bisect the angles.
400
What do the sides of a rectangle add up to?
The SIDES could ADD to anything. ( The angles add to 360 degrees. )
400
One side of a square is 5 cm. What is the length of the diagonal of the square?
5 radical 2 ( 5 times the square root of 2 )
400
I am a quadrilateral that has two pairs of congruent adjacent sides. What am I?
A kite.
500
In parallelogram ABCD, diagonals AC and BD intersect at E. If angle A = 85, and AE = 3x + 10, and EC = 7x - 30, Find the measure of angle C and the value of x.
Angle C is 85 degrees because opposite angles in a parallelogram are congruent, and x = 10, because the diagonals bisect each other.
500
In rhombus ABCD, the diagonals are drawn and intersect at E. If AC = 20, and BD = 48, what is the measure of AB?
Use the fact that the diagonals bisect each other and are perpendicular. Each right triangle has legs of 10 and 24. Use the pythagorean theorem to figure out that AB = 26.
500
If a rectangle and a rhombus had a child, what would it look like? Why?
It would be a square because a square has all of the properties of a rectangle and a rhombus.
500
The diagonal of a square is 6 cm. What is the length of one side of the square? Leave your answer in simplest radical form.
The square root of 18, which is 3 radical 2.
500
A quadrilateral has these properties: Diagonals bisect each other. Diagonals are congruent. Choose any of the following that it could be. I.) isosceles trapezoid II.) rhombus III.) rectangle IV.) parallelogram V.) square
III.) rectangle and V.) square