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Geometry Review - Ch. 6
Name __________________________________
For each of the following shapes, state the definition, draw a picture, and choose the letter that corresponds to the properties.
Parallelogram
Definition: _________________________________________
CHOICES FOR PROPERTIES:
Picture:
A. Opposite sides are congruent
B. Opposite angles are congruent
Properties: 1. ______ 2. ______ 3. ______ 4. ______
C. Consecutive angles are supplementary
Rhombus
D. Diagonals bisect each other
Definition: _________________________________________
E. Diagonal bisect the corner angles
Picture:
F.
Properties: 1. ______ 2. ______ 3. ______ 4. ______
Diagonals are congruent
G. Diagonals are perpendicular
5. ______ 6. ______
Rectangle
Square
Definition: _________________________________________
Definition: _________________________________________
Picture:
Picture:
Properties: 1. ______ 2. ______ 3. ______ 4. ______
Properties: 1. ______ 2. ______ 3. ______ 4. ______
5. ______
5. ______ 6. ______ 7. ______
Study the Venn Diagram which relates all of these quadrilaterals..
Trapezoid
Definition: _________________________________________
Picture:
An isosceles trapezoid has _____________________________
The base angles of an isosceles trapezoid are ______________
To find the length of the midsegment, you _______ the bases
together and divide by ______.
Answer true or false.
1. Every rectangle is a square ______________________
2. Every square is a rectangle ___________________________
3. Every parallelogram is a rhombus_________________
4. Every rhombus is a rectangle__________________________
5. Every square is a quadrilateral____________________
6. Every square is a rhombus ____________________________
7. The diagonals of a rectangle are perpendicular _______
8. The diagonals of a square are perpendicular _____________
9. The diagonals of a rectangle are congruent ___________ 10. The diagonals of a rhombus are congruent _______________
11. The opposite sides of a parallelogram are congruent________ 12. The opposite angles of a parallelogram are supplementary_______
13. The diagonals of all parallelograms bisect each other _______ 14. The diagonals of all parallelograms are congruent ________
Name the following segments or angles in the trapezoid. Use the correct notation!
15. Two Bases: ____________
16. Two Legs: ____________
17. Midsegment: ____________ 18. Two pairs of Base Angles: _________ & _________
For each PARALLELOGRAM, find each length or measure.
19.
20.
21.
A
mC ______
mB ______
m1 ______
m2 _____
XO______
XZ _____
BC = ______
DC = ______
m3 ______
m4 _____
OY ______
WY _____
For each RHOMBUS, find each length or measure.
22.
23.
24.
mC ______
mB ______
m1 ______
m2 _____
m1 ______
m2 _____
BC = ______
DC = ______
m3 ______
m4 _____
m 3 ______
m4 _____
For each RECTANGLE, find each length or measure.
25.
26.
27.
m1 ______
m2 ______
m1 ______
m2 _____
XO_____
XZ _____ OY _____
BC = ______
DC = ______
m3 ______
m4 _____
WY _____
m1 ____ m2 ____
For each SQUARE, find each length or measure.
28.
29.
30.
m1 ______
m2 ______
m1 ______
m2 _____
m1 ______
m2 _____
BC = ______
DC = ______
m3 ______
m4 _____
m3 ______
m4 _____
m2 _____
For each TRAPEZOID, find each length or angle measure
31.
32.
mR ______
mT ______
33.
mP _____
mS ____
m1 ______
mA _____
PA _____
m3 _____ m4 ______ y = ______
Name all the quadrilaterals that have each property. Choices: parallelogram, rhombus, rectangle, square. There will be more than one answer!
34. All angles congruent _______________________________________
35. Opposite angles are congruent _______________________________________
36. The diagonals are perpendicular ______________________________
37. The diagonals bisect each other ______________________________________
Using the properties of each shape to write and solve an algebraic equation for each picture.
Rhombus
Parallelogram
38.
39.
Rectangle
40.
Equation:
Equation:
Equation:
x = _______ mABC = ______ mBCD = ______
x = _______
x = _______
Square
Trapezoid
IsoscelesTrapezoid
41.
42.
43.
Equation:
Equation:
Equation:
x = _______
x = _______
x = _______
MATCH the name of each polygon with the number of sides.
44. Octagon
45. Triangle
A. 3 sides
E. 7 sides
46. Quadrilateral
47. Hexagon
B. 4 sides
F. 8 sides
48. Nonagon
49. Pentagon
C. 5 sides
G. 9 sides
50. Heptagon
51. Triangle
D. 6 sides
H. 10 sides
State whether the figure is a polygon. If so, classify (Name) the polygon by its number of sides.
52.
53.
54.
55.
56.
Name the following for the pentagon shown.
57. Two sides adjacent to RS _______________
58. Two vertices consecutive to T ______________
59. Two angles consecutive to T ____________ 60. Two diagonals with endpoint R _____________
61. The sum of the angles of a TRIANGLE is ________
62. The sum of the angles of a QUADRILATERAL is ________
Use the formulas to find the measure of the missing angle or the value of x.
63.
64.
65.
66.
mD= ______
mD= ______
x = ______
x = ______