Download - Stevenson High School

Geometry
6.4 – 6.7 Quest Retake Review
1.
Name
Date
A.
The diagonals of a rhombus must
B.
The diagonals of a rectangle must
C.
The diagonals of a square must
D.
The diagonals of a parallelogram must
Hour
and
.
.
,
and
.
.
2. In the square ABCD, determine the measure of each angle:
a. 𝑚∠𝐴𝐷𝐶 =
b. 𝑚∠𝐴𝐷𝐵 =
c. 𝑚∠𝐵𝐸𝐶 =
d. 𝑚∠𝐵𝐶𝐴 =
e. 𝑚∠𝐴𝐶𝐵 =
f. 𝑚∠𝐵𝐶𝐷 =
3. KLMN is a RECTANGLE. Find the values of x, y, and z.
K
L
45
4y - 15
7y -24
(5z + 25)
N
4. If 𝐴𝐵||𝐷𝐶 𝑎𝑛𝑑 𝐴𝐷 ≅ 𝐵𝐶, then ABCD is a
6x + 9
o
M
.
̅̅̅̅
𝐴𝐷 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐶 are
.
̅̅̅̅
𝐴𝐵 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐶 are
.
̅̅̅̅
𝐴𝐵 𝑎𝑛𝑑 ̅̅̅̅
𝐷𝐶 are
.
̅̅̅̅
𝐴𝐶 𝑎𝑛𝑑 ̅̅̅̅
𝐵𝐷 are
.
For #5-8, draw the diagonals and provide the appropriate marks to designate the properties of the diagonals for that
shape.
5. Parallelogram
6. Rhombus
7. Square
8. Rectangle
Property
Parallelogram
Rectangle
Rhombus
Square
Kite
All sides congruent
Both pairs of opposite sides are parallel
Both pairs of opposite angles are congruent
Exactly one pair of opposite sides are parallel
All angles are congruent
Exactly one pair of opposite angles are congruent
Diagonals are perpendicular
Diagonals are congruent
Diagonals bisect each other
9. Fill in the appropriate check marks for the quadrilateral properties.
10. Fill in each blank with always, sometimes, never.
a. A rectangle
has congruent diagonals.
b. Angles of a parallelogram are
congruent to each other.
c. A rectangle
has 4 congruent angles.
d. A parallelogram
has congruent diagonals.
e. A rhombus
has 4 congruent sides.
f. Diagonals of a rhombus are
perpendicular.
g. A rhombus
has consecutive angles that are supplementary.
h. A rhombus
has 4 right angles.
i. Diagonals of a rectangle are
perpendicular.
j. Diagonals of a square are
perpendicular.
k. Parallelograms
have 4 congruent sides and 4 congruent angles.
11. ABCD is a quadrilateral. Draw a picture.
What is the most precise name for the quadrilateral? Explain how you know.
AB = 5
BC= 5
CD= 9
AD= 9
slope of AB= 14
slope of BC= -4
slope of CD = 4
slope of AD= ½
11. Name
Explain:
12. ABCD is a quadrilateral. Draw a picture.
What is the most precise name for the quadrilateral? Explain how you know.
12. Name
AB = 5
BC= 5
CD= 5
AD= 5
Explain:
slope of AB = ½
slope of BC= -2
slope of CD = ½
slope of AD= -2
13. ABCD is a quadrilateral. Draw a picture.
What is the most precise name for the quadrilateral? Explain how you know.
13. Name
Trapezoid
Isosceles
Trapezoid
AB = 6
BC= 10
CD= 6
AD= 10
slope of AB= 3
slope of BC= -3
slope of CD= 3
slope of AD= -3
Explain:
14.
Find the value of x, m∠T, and m∠S in the isosceles
trapezoid.
15. Find the value of angles 1, 2 and 3 in the rectangle.
38o
1
3
2
16. Find the values of x and y in the rhombus
17. In the kite, find the value of angles A and D.
75o
55o
115o
y
x
18. RECT is a rectangle. If RA = 5x +12 and TE = 5x +84 , can it also be classified as a square?
a) Solve for x
b) Explain why it is or is not a square.
R
E
A
T
C
Rectangle/Parallelogram: A = bh
Trapezoid: A =
h(b1 + b2 ) 1
= h(b1 + b2 )
2
2
bh 1
= bh
2 2
d ×d 1
Kite/Rhombus: A = 1 2 = d1 × d2
2
2
Triangle: A =
Find the area, or missing value given the area, of each figure.
19.
20.
21. ST = 4, PR = 12
22. If the area of parallelogram EFGH is 112 square
meters, what must the value of x be?
23.
24.