Parallelograms
Rhombuses
Rectangles
Squares
Kites and Trapezoids
Area
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
How do you prove a rectangle is a square?
Show it has 2 congruent adjacent sides.
All sides are congruent.
Diagonals are perpendicular,
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
100
Find the area.
We need to divide the shape
10*2=20
(9-2)*(10-6)=28
20+28=48 cm²
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
Can a rhombus be a rectangle? Explain why or why not.
Yes, when it is a square as a square is also a rectangle.
200
In rectangle ABCD, AC = 7x and BD = 3x + 20. What is the value of x? Explain
Diagonals are congruent
AC=BD
7x=3x+20
x = 5.
200
How do you prove a rhombus is a square?
Daily Double
Show it has ONE right angle. Also accpetable, Show it has 4 right angles.
200
A quadrilateral has the following properties: Its diagonals bisect the angles. Its diagonals are not congruent. What could the quadrilateral be?
A rhombus and a square both bisect opposite angles
A squares diagonals are congruent a Rhombus is not
The quadrilateral is a Rhombus
200
A rectangular garden has a surrounding 5 meters wide path - green area. If the entire area is 1Km, what is the length and width of the garden?
A=lw
1 Km =1000 meters
1000=20l
50=l
Deduct the width of the path around the garden, (5*2) from each of the above measures to get the
l of garden=50-10=40 meters
w=20-10=10 meters
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 s
ides 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 angles CBD? Why?
Daily Double
Consecutive angles are supplementary - or by same side interior 
m<ABC=180-72=108
The Diagonals of a Rhombus bisect opposite angles
m<CBD=108/2=54
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
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
All 4 angles are congruent,
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
300
The area of a kite A=1/2(d1d2)
d1 is the non-vertex diagonal and it is bisected by the vertex diagonal so both pieces =8cm d1=16
d2 use the Pythagorean theorem to solve
√17²+8²=15
√10²-8²=6
d2=15+6=21
A=1/2 16*21=168 cm²
400
To prove a quadrilateral is a parallelogram, how could you use the definition and/or at least 2 properties and formulas you could use to prove this.
I.) Both pairs of opposite sides are congruent. Distance
II.) Both pairs of opposite sides are parallel. Slope - parallel slopes are =
III.) One pair of sides are parallel and congruent. Slope and Distance
IV.) The diagonals bisect each other. Either distance showing segments of diagonals are congruent or Midpoint showing that they share the same midpoint.
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, express in radical form? Why?
Sides of a square are congruent, thus use the Pythagorean Theorem √5²+5²=√2(*5²=5√2
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.
An isosceles trapezoid.
400
The area of a trapezoid is 50 cm²
The height is 5 cm, and one base is 7 cm.
What is the measure of the other base
A=1/2(b1+b2)h
50=1/2 * 5(7+b)
20=7+b
13 cm = b
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 state why and the value of x.
Opposite angles are congruent.
M<C=m<A= 85 degrees -
The diagonals bisect each other.
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 bisecters of each other and are perpendicular. 
Thus ABE is a Right Triangle
Use the Pythagorean Theorem
AB=√(20/2)²+(48/2)²=26
500
If a rectangle is crossed 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? Leave your answer in simplest radical form, explain your work.
The sides of a square are congruent.
6²=2x²
36=2x²
18=x²
3√2=x
500
A quadrilateral has these properties: Diagonals are perpendicular to each other. Adjacent sides are congruent. What type of quadrilateral could the figure be?
Kite or Rhombus or Square
500
Daily Double
The area formula of a regular polgyon is A=1/2aP
Where a is the apothem a
nd P is the perimeter.
What is the area of the following polygon?
a=15
P=18*5=90
A=1/2*15*90=675 units²