Parallelograms
Rhombuses
Rectangles
Squares
?
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
In order for a rectangle to be a square, what must be present?
4 congruent sides
100
What is the Pythagorean Theorem? For what shape or shapes can it be used on?
a^2 + b^2 = c^2 (right triangles)
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 or "same-side" 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
In order for a rhombus to be a square, what must be present?
At least ONE right angle. (Because if it has one, it will have 4...)
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. a.) rhombus b.) rectangle c.) parallelogram d.) square
a.) 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. 6x - 2 = 2x + 12
300
In rhombus ABCD, diagonals AC and BD intersect at E. If the measure of angle BAD = 72, what is the measure of angle CDA? BONUS 50 POINTS: If AE = 14, what other segments are congruent to AE?
Angle CDA = 108 (same side interior angles are supplementary) BONUS: BE, CE, and DE (Diagonals in a rhombus are congruent to one another, therefore, the portions of the diagonals connected from the corners to the midpoint of the diagonals are also congruent.)
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 (diagonals are congruent)
300
Name 7 of the 8 properties of a square. BONUS 100 POINTS: Name all 8.
DIAGONALS: 1) perpendicular bisectors 2) congruent 3) angle bisectors 4) form 4 isosceles right triangles SIDES: 5) all 4 sides are congruent 6) opposite sides are parallel ANGLES: 7) all 4 angles are congruent 8) consecutive/same side angles are supplementary.
300
When naming the points and sides of a triangle, which one gets the capital letter and which one gets the lower case letter? How do you know how to name the sides of a triangle?
Angles get the capital letters and sides get the lower case letters. To name the sides of a triangle, look at the angle opposite of the side you are trying to name.
400
Name the 5 properties that are true for all parallelograms.
Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Same-side interior angles are supplementary. Diagonals bisect each other.
400
Name the properties that the diagonals of a rhombus have.
Diagonals are perpendicular bisectors. Diagonals are angle bisectors.
400
What do the angles of a rectangle add up to? BONUS 100 POINTS: What do the sides of a rectangle add up to?
The angles add to 360 degrees. BONUS: The sum of the sides depend on the measures of the sides. They could add to anything!
400
One side of a square is 5 cm. What is the length of the diagonal of the square? Use the Pythagorean Theorem, and simplify the radical expression.
sqrt 50 = 5 sqrt 2
400
My diagonals bisect angles and form right angles where they meet. What am I?
A rhombus
500
In parallelogram ABCD, diagonals AC and BD intersect at E. If angle BAD = 85 degrees, and AE = 3x + 10, and EC = 7x - 30, find the measure of angle DCB and the value of x. (State what property you used).
Angle DCB is 85 degrees (opp. angles are congruent), and x = 10 (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 angle AEB?
90 degrees. The diagonals of a rhombus are perpendicular bisectors, therefore, angle AEB and all other angles formed at the intersection of the diagonals will be 90 degrees. (Make sure you read the question to understand what it is asking...)
500
If a rectangle and a rhombus had a child, what would it look like? Explain your reasoning.
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. We know that squares have 4 equal sides. Use the Pythagorean Theorem to find the measure of one of the sides. (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. a.) rhombus b.) rectangle c.) parallelogram d.) square
b.) rectangle and d.) square
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