Parallelograms
Rhombuses
Rectangles
Squares
Kites and Trapezoids
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? Explain why.
By definition the sides of a Rhombus are congruent.
MN=NO
24=2x+6
x = 9
100
Name the 2 properties that the diagonals of a rectangle have.
Diagonals are congruent.
Diagonals bisect each other.
100
What is the definition of a square?
A square is a quadrilateral with 4 congruent sides and 4 90 degree angles.
100
In a trapezoid, the upper base is 12, and the lower base is 30. What is the midsegment of the trapezoid? Explain your set up.
The midsegment is the average of the bases.
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. What is the value of x?
Add the expressions and set them equal to 180 degrees.
( Consecutive Angles are Supplementary )
(2x+40)+(3x-10)=180
x=30
200
Is a rhombus always a square?
No.
200
In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x? Explain
Diagonals are congruent so AC=BD.
7x=3x+20
x = 5.
200
Is this statement sometimes, always or never true?
A rhombus is a square.
Sometimes true. If a rhombus has 4 90 degree angles, then it will be a square. If a rhombus as any other angle measures, it won't be a square.
200
A quadrilateral has the following properties: One diagonal bisects one pair of opposite angles. It's diagonals are not congruent. It's diagonals are perpendicular.
The quadrilateral is a kite.
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. What is the length of side AB?
The opposite sides of a parallelogram are congruent. Set the expressions for sides AD and BC equal to one another.
(2x+12)=(6x-2)
x=7
AB=16
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? Why?
Consecutive angles are supplementary - or by same side interior are supplementary.
m<ABC=180-72=108
The Diagonals of a Rhombus bisect opposite angles so m<CBD=108/2=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 BC? Explain,.
Diagonals are congruent and bisect each other so AE=DE.
4x+20=9x+4
x = 4
BC=7(4)+12= 40
300
Name at least 5 properties of a square.
(DIAGONALS): perpendicular, congruent,
bisect each other, bisect the angles
(SIDES): all 4 sides are congruent
(ANGLES: All 4 angles are congruent, all 4 are 90 degrees
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.) the diagonals bisect each other
400
To prove a quadrilateral is a parallelogram, how could you use the definition to prove this?
Prove that both sets of opposite sides are parallel.
400
Name the 3 properties that the diagonals of a rhombus have.
Diagonals bisect each other
Diagonals are perpendicular
Diagonals bisect the opposite angles
400
What is the sum of the interior angles of a rectangle? Why?
What is the measure of an exterior angle of a rectangle? Why
By Polygon interior angle sum? (4-2)180=360
Or all angles of a rectangle are 90° so 4(90)=360
Either by Exterior Polygon angle sum 360/4=90
As each interior angle is 90° and forms a linear pair with the exterior then by Congruent Supplements the exterior angle is 90°
400
One side of a square is 5 cm. What is the length of the diagonal of the square to the nearest tenth?
Sides of a square are congruent, thus use the Pythagorean Theorem
√5²+5² = 7.1 cm
400
I have congruent diagonals, the slopes of one set of the opposite side are congruent and the other set of sides are congruent, and my base angles are congruent. What shape am I?
An isosceles trapezoid.
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, state why and then find the value of x.
Opposite angles are congruent. m<C=m<A= 85 degrees.
The diagonals bisect each other so AE=EC.
3x+10=7x-30
x = 10
500
In rhombus ABCD, the diagonals are drawn and intersect at E. If AC = 20, and BD = 48, what is the measure of AB? Explain.
Use the fact that the diagonals are perpendicular bisectors of each other and are perpendicular. 
Thus ABE is a Right Triangle so you can use the Pythagorean Theorem.
AB=√(20/2)²+(48/2)²=26
500
If a rectangle is combined with a rhombus what type of quadrilateral would be the result?
A square as it shares both the properties of a rhombus and a rectangle.
500
The diagonal of a square is 6 cm. What is the length of one side of the square? Round to the nearest tenth.
The sides of a square are congruent.
6²=2x²
36=2x²
18=x²
4.2=x
500
What is the length of BD? Round to the nearest tenth.
After setting up two Pythagorean Theorem problems, BD = 14.3.