Quadrilateral Properties-Geometry

Parallelograms

100

Name a property that the diagonals of a parallelogram have.

The diagonals bisect each other.

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 )

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.

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, and x = 10, b/c the diagonals bisect each other.

Rhombus

100

In Rhombus MNOP, MN = 24, and NO = 2x + 6. What is the value of x?

x = 9

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.

300

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

Angle CED = 54, use the right triangles, and the fact that the angles bisect the corner angles.

400

Name the 3 properties that the diagonals of a rhombus have.

diagonals bisect each other diagonals are perpendicular diagonals bisect the angles

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.

Rectangles

100

Name the 2 properties that the diagonals of a rectangle have.

They are congruent and bisect each other.

200

In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x?

x = 5.

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

400

What do the sides of a rectangle add up to?

The SIDES could ADD to anything. ( The angles add to 360. )

500

If the area of a rectangle is 60 and one side length is 12.  What is the measure of the diagonal.

13

Squares

100

True or False.  All squares are rectangles.

True

200

True or False.  All rectangles are squares.

False

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 )

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.

Other

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

What is the sum of the exterior angles of an octagon

360 degrees

300

Name the polygon whose interior angles sum up to 1800 degrees

dodecagon

400

What is the measure of 1 interior angle of a regular quadrilateral.

90 degrees