Download Geo Ch 8 Review

Name: ____________________________________ Class: _______________ Date: __________
Geometry Chapter 8 Review
Fill in the blank with always, sometimes or never.
1. Rectangles are ______________ parallelograms
2. Squares are _______________ rectangles
3. Rectangles are _______________squares
4. Quadrilaterals are _______________ rectangles
5. Rectangles are ________________ quadrilaterals
6. If two sides of a quadrilateral are perpendicular, then the quadrilateral is ________________a rectangle.
7. Trapezoids are ___________________ parallelograms.
8. If a quadrilateral has opposite sides that are parallel and congruent, then the quadrilateral is _____________rectangle.
9. The diagonals of an isosceles trapezoid are _________________ congruent.
Short Answer
10. Find the sum of the measures of the interior angles and exterior angles:
a. pentagon
b. dodecagon
Sum of interior ________
Sum of interior ________
Sum of exterior ________
Sum of exterior ________
11. Find the measures of each exterior angle and interior angle:
a. Regular decagon.
b. regular hexagon
each interior ________
each interior ________
each exterior ________
each exterior ________
12. Find x and y so that quadrilateral LPHS is a parallelogram.
L
30° 56°
x
S
y
H
P
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.
13.
,
,
,
; Distance and Slope Formulas
y
x
Determine whether the quadrilateral is a parallelogram. Justify your answer.
14.
15.
16.
17.
18.
19.
Use parallelogram MOPQ to answer questions 20-24.
21. MN || _____
22. r  _____
23. mQ  _____
24. mP  _____
N
M
20. MN  _____
2r
Q
3r-30
P
Use rectangle ABCD to answer questions 25-27.
25. If AG  2 j  35 and AC  4 j  22 , find BD
A
B
G
D
26. If
and

, find
.

27. If mBAC  x 2  9  and mACD   2 x  44   , find mACB .
28. For trapezoid JKLM, A and B are midpoints of the legs. Find AB, mL , and mK .
26
J
K
A
B
75°
M
L
31
29. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.
M
L
37.5
A
B
47
J
K
30. In rhombus TUVW
T
U
a. If mTUW  58 , find
.
O
W
V
b. If mUOV   5x  35  , find x.
c. If TU  7 x  8 , and UV  4 x  22 , what is the perimeter of TUVW?
C
Determine what type of quadrilateral ABCD is. List all that apply: Quadrilateral, Parallelogram,
Rectangle, Rhombus, Square, Trapezoid, Isosceles Trapezoid
31. A(-9, 1), B(2, 3), C(12, -2), D(1, -4)
y
x
32. A(1, 3), B(7, -3), C(1, -9), D(-5, -3)
y
x
33. A(-4, -5), B(1, -5), C(-2, -1), D(-7, -1)
y
x
34. A(-1, 1), B(-5, -3), C(-4, -10), D(6, 0)
y
x
Name the missing coordinates in terms of the given variables.
35. Parallelogram
36. Rectangle
37. Rhombus
y
y
B(c,?)
y
C(?,a)
B(0, a)
B(0, b)
C(?,?)
C(-a,0)
A(?,?)
x
O
O A(0,0)
D(2b, 0) x
O A(0,0)
__________________
D(c, 0) x
__________________
39. Using the figure below, write a coordinate proof for the following condition.
The diagonals of a rectangle are congruent.
y
J
K
L
M
x
40. Using the figure below, write a coordinate proof for the following condition.
The median of a trapezoid is parallel to the bases.
y
P
Q
X
Y
S
R
S (0, 0); P (–b, c); Q (a + b, c); R (a, 0)
x
D(0, -b)
___________________
Check the appropriate boxes
Quadrilateral
Has 4 Sides
Both pairs of opposite
sides are parallel
Exactly one pair of
opposite sides are parallel
Both pairs of opposite
sides are congruent
Exactly one pair of
opposite sides are
Congruent
All sides are congruent
Opposite angles are
congruent
All angles are right angles
Diagonal forms two
matching triangles
Diagonal forms two
matching isosceles
triangles
Diagonals are congruent
Diagonals bisect the
opposite angles
Diagonals are
perpendicular
Diagonals bisect each
other
Consecutive angles are
supplementary
Sum of the interior angles
is 360
Parallelogram Rectangle
Rhombus
Square
Isosceles
Trapezoid