Geometry Review Chapter 9

advertisement
9.9 Worksheet
Honors Geometry
Quadrilateral Review #1
Name ___________________
Date ________Period ______
I. Complete the chart by putting abeside each property that applies.
Property
All sides 
Opposite sides 
Opposite sides //
Opposite angles 
All angles are right <s
Diag. bisect each other
Diagonals are 
Diagonals are 
Diags. bisect opp. angles
Parallelogram
Rhombus
Rectangle
Square
II. Based on the markings, decide if each figure is a parallelogram. Justify your answer.
2.
3.
4.
5.
6.
7.
III. Find the values of the variables for each figure.
8.
9.
(7y - 2)
10. AC= 7x – 15; BD= 4x + 15
3x
4x+1
y
9y
(2x + 33)
3x
11.
12.
2x
2
(x – 12x)
B
D
C
13.
y
(4y-10)
A
3x
24
13
x
34
14.
y
15.
16.
101
y
x
y
x
x
65
79
48
17.
18.
y
50
9x
115 
z
x
19.
3x 
11x
20.
(8y + 1)
x + 2
21.
22.
x
17
y˚
6x
2x - 1
y
(2y – 1)
x
5
(y + 5)
(4y – 2)
11
IV. #23-28, draw a picture and show your work.
23. In MATH, mM=X2-7X,
mT=X+48. Find mH.
25. The perimeter of square MNOP is 60.
Find MO.
24. In rectangle EFGH, EG is 25,
EH=24. Find mHEG.
26. In rhombus JKLN, KL is 10,
diagonal JL=16. Find NK.
27. Find the perimeter of rhombus JACK if AK=80, JC=18. Find mAJK.
28. In parallelogram ABCD the mB = (x2) ˚ and mD = (9x + 36) ˚.
Find the value of x and the mC.
T
O
29. Given: H  E; Parallelogram OTEL
Prove: HO  TE
H
E
L
30. Given: Isosceles Trapezoid TRAP with TR  PA
Prove: 1  2
R
A
Z
2
1
T
P
31. Set up and prove the following theorem: If one diagonal of a parallelogram bisects two
angles of the parallelogram, then the parallelogram is a rhombus.
32. Give the 'most specific' name for the quadrilateral ABCD. Then prove that your
answer is correct by coordinate proof. A(-2, 2) B(1, 0) C(3, -3) D(0, -1).
33. Find the coordinates for A and S without introducing any new variables.
Then complete the proof.
I (a, 2b)
Given: LISA is a rhombus
Prove: LI  SA
L (0, b)
S
A
D
34.
Given: ABCD; DE  AC ; BF  AC
Prove: DEBF is a parallelogram
F
3
1
2
m=
y2  y1
x2  x1
4
6
E
A
d = (x2  x1 )2  ( y2  y1 )2
5
C
B
x x y y
midpoint =  1 2 , 1 2 

2
2

****You must show the calculation of each distance, slope and midpoint.
Review all of your unit 9 worksheets.
Take extra time to look over the “proofs” from unit 9.
Proof portion on Unit 9 Test is tomorrow in class.
Download