Quadrilateral Properties-Geometry

Parallelograms

100

In parallelogram ABCD, which interior angles are congruent?

Angle A and C

Angle B and D

200

Name a property that the diagonals of a parallelogram have.

Diagonals bisect eachother 

300

If ABCD is a parallelogram, and AB = 3x - 5, and BC = 6x - 2, and AD = 2x + 12. Set up the equation used to solve the problem.

Set the expressions for sides BC and AD equal to one another.

6x -2 = 2x +12

400

To prove a quadrilateral is a parallelogram, which of the following would NOT be sufficient? 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.

IV) The diagonals are not congruent, they BISECT EACH OTHER.

500

In parallelogram ABCD, diagonals AC and BD intersect at E. If AE = 3x + 10 and EC = 7x - 30, Find the value of x.

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

Rhombuses

100

True or False: All rhombuses have congruent diagonals 

False!

200

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

x = 9

300

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.

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

What do the interior angles of a rectangle add up to?

360 degrees

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

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

They are congruent and bisect each other.

500

If we combine the properties of a rectangle and a rhombus, what shape would we make?

It would be a square b/c a square has all of the properties of a rectangle and a rhombus.

Squares

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.

200

How do you prove a rhombus is a square?

Show it has ONE right angle. Also accpetable, Show it has 4 right angles.

300

Name at least 5 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.

400

True or false: All rectangles are squares

False, all squares are rectangles 

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.

4.2

?

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

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

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

I have congruent diagonals, the slopes of two of my sides are equal, and the slopes of my other two sides are opposites of each other, namely -1/2 & 1/2. What am I?

An isosceles trapezoid.

500

What does CPCTC stand for?

Corresponding parts of congruent triangles are congruent