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Parallelograms
Rhombi
Rectangles
Squares
Mixed Review
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
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 cm, and the lower base is 30 cm. What is the length of the midsegment of the trapezoid?

21 cm

200

If ABCD is a parallelogram and the measure of angle A = 2x + 40 and the measure of angle B = 3x - 10, how could we find the value of x? Explain how you would set up an equation, if possible. 

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.
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

Double Jeopardy!!

1.) What is the formula that is used to find the sum of the interior angle measures of a regular polygon?

2.) If the sum of the interior angles of a polygon is 3780 degrees, how many sides does it have?

1.) (n-2)*180/n

2.) n=23

300

If ABCD is a parallelogram, and AB = 3x - 5, BC = 6x - 2, and AD = 2x + 12, how could we find AB? Explain the equation used to solve the problem.

Set the expressions for sides BC and AD equal to one another to find x, and then plug x into AB = 3x-5!

300

In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72 degrees, what is the measure of angle CBE?

Angle CBE = 54 degrees

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
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, we must 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 three properties that the diagonals of a rhombus have.

1.) diagonals bisect each other

2.) diagonals are perpendicular

3.) diagonals bisect opposite angles

400
What do the sides of a rectangle add up to?
The SIDES could ADD to anything. ( The angles add to 360. )
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

Six angles of a heptagon measure 107 degrees, 139 degrees, 131 degrees, 110 degrees, 145 degrees, and 128 degrees. What is the measure of the seventh angle?

140 degrees

500

In parallelogram ABCD, diagonals AC and BD intersect at E. If the measure of angle A = 85 degrees, AE = 3x + 10, and EC = 7x - 30, find the measure of angle C and the value of x.

Angle C is 85 degrees, and x = 10, b/c 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 quadrilateral DEFG is a rectangle, the measure of angle DEG = (4x-5) degrees and the measure of angle FGE = (6x-21) degrees. What is the measure of angle DGE?

measure of angle DGE = 63 degrees

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 the following properties: diagonals bisect each other and 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