Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry Blizzard Bag Day 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
¾¾
¾
®
____
¾¾
¾
®
1. Draw and label a pair of opposite rays FG and FH .
a.
c.
b.
d.
____
2. K is the midpoint of JL . JK = 6x and KL = 3x + 3 . Find J K, KL, and J L.
a. J K = 1, K L = 1, J L = 2
c. J K = 12, KL = 12, J L = 6
b. J K = 6, K L = 6, J L = 12
d. J K = 18, KL = 18, J L = 36
____
3. The tip of a pendulum at rest sits at point B. During an experiment, a physics student sets the pendulum in
motion. The tip of the pendulum swings back and forth along part of a circular path from point A to point C.
During each swing the tip passes through point B. Name all the angles in the diagram.
a.
b.
ÐAOB, ÐBOC
ÐAOB, ÐCOB, ÐAOC
c.
d.
1
ÐAOB, ÐBOA, ÐCOB, ÐBOC
ÐOAB, ÐOBC , ÐOCB
Name: ________________________
____
ID: A
4. Tell whether ÐFAC and Ð3 are only adjacent, adjacent and form a linear pair, or not adjacent.
a.
b.
c.
adjacent and form a linear pair
only adjacent
not adjacent
____
5. An angle measures 2 degrees more than 3 times its complement. Find the measure of its complement.
a. 68°
c. 23°
b. 272°
d. 22°
____
6. Name all pairs of vertical angles.
a.
b.
c.
d.
ÐMLN and ÐJLM ; ÐJLK and ÐKLN
ÐJLK and ÐMLN ; ÐJLM and ÐKLN
ÐJKL and ÐMNL; ÐJML and ÐKNL
ÐJLK and ÐJLM ; ÐKLN and ÐMLN
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Name: ________________________
____
ID: A
7. Find the coordinates for the image of DEFG after the translation (x, y) ® (x – 6, y + 2). Draw the image.
a.
c.
b.
d.
3
Name: ________________________
____
8. An animated film artist creates a simple scene by translating a kite against a still background. Write a rule for
the translation of kite 1 to kite 2.
a.
b.
____
ID: A
(x, y) ® (x – 6, y + 6)
(x, y) ® (x + 6, y – 6)
c.
d.
(x, y) ® (x – 2, y + 2)
(x, y) ® (x + 2, y – 2)
c.
d.
R, P, and G
R, G, and N
9. Name three collinear points.
a.
b.
P, G, and N
R, P, and N
____ 10. Find the next item in the pattern 2, 3, 5, 7, 11, ...
a. 13
c.
b. 12
d.
4
15
17
Name: ________________________
ID: A
____ 11. The table shows the population 65 years and over by age and sex according to the US Census Bureau, Census
2000 Summary file. Make a conjecture based on the data.
Women
Men
a.
b.
c.
d.
Population 65 Years and Over by Age and Sex: 2000
(numbers in thousands)
65 to 74 years
75 to 84 years
85 years and over
10,088
7,482
3,013
8,303
4,879
1,227
Women outnumbered men in the 65 years and over population.
Men outnumbered women in the 65 years and over population.
There are more 65 years old and over in 2000 than in previous years.
There are fewer 65 years old and over in 2000 than in previous years.
____ 12. A gardener has 26 feet of fencing for a garden. To find the width of the rectangular garden, the gardener uses
the formula P = 2l + 2w , where P is the perimeter, l is the length, and w is the width of the rectangle. The
gardener wants to fence a garden that is 8 feet long. How wide is the garden? Solve the equation for w, and
justify each step.
P = 2l + 2w
26 = 2(8) + 2w
26 = 16 + 2w
-16 = -16
10 = 2w
10 2w
=
2
2
5=w
w=5
a.
b.
Given equation
[1]
Simplify.
Subtraction Property of Equality
Simplify.
[2]
Simplify.
Symmetric Property of Equality
[1] Substitution Property of Equality
[2] Division Property of Equality
The garden is 5 ft wide.
[1] Simplify
[2] Division Property of Equality
The garden is 5 ft wide.
c.
d.
____ 13. Identify the property that justifies the statement.
AB @ CD and CD @ EF . So AB @ EF .
a. Reflexive Property of Congruence
c.
b. Substitution Property of Equality
d.
5
[1] Substitution Property of Equality
[2] Subtraction Property of Equality
The garden is 5 ft wide.
[1] Subtraction Property of Equality
[2] Simplify
The garden is 5 ft wide.
Symmetric Property of Congruence
Transitive Property of Congruence
Name: ________________________
ID: A
____ 14. Use the given plan to write a two-column proof.
Given: mÐ1 + mÐ2 = 90°, mÐ3 + mÐ4 = 90°, mÐ2 = mÐ3
Prove: mÐ1 = mÐ4
Plan: Since both pairs of angle measures add to 90°, use substitution to show that the sums of both pairs are
equal. Since mÐ2 = mÐ3, use substitution again to show that sums of the other pairs are equal. Use the
Subtraction Property of Equality to conclude that mÐ1 = mÐ4.
Complete the proof.
Proof:
Statements
1. mÐ1 + mÐ2 = 90°
2. [1]
3. mÐ1 + mÐ2 = mÐ3 + mÐ4
4. mÐ2 = mÐ3
5. mÐ1 + mÐ2 = mÐ2 + mÐ4
6. mÐ1 = mÐ4
a.
b.
c.
d.
Reasons
1. Given
2. Given
3. Substitution Property
4. Given
5. [2]
6. [3]
[1] mÐ3 + mÐ4 = 90°
[2] Substitution Property
[3] Subtraction Property of Equality
[1] mÐ5 + mÐ6 = 90°
[2] Substitution Property
[3] Subtraction Property of Equality
[1] mÐ3 + mÐ4 = 90°
[2] Subtraction Property of Equality
[3] Substitution Property
[1] mÐ5 + mÐ6 = 90°
[2] Addition Property of Equality
[3] Substitution Property
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Name: ________________________
ID: A
____ 15. Use the given flowchart proof to write a two-column proof of the statement AF @ FD .
Flowchart proof:
AB = CD;
BF = FC
Given
AB + BF =
FC + CD
Addition Property
of Equality
AB + BF = AF
FC + CD = FD
Segment Addition
Postulate
AF = FD
AF @ FD
Substitution
Definition of
congruent segments
Complete the proof.
Two-column proof:
Statements
1. AB = CD; BF = FC
2. [1]
3. [2]
4. AF = FD
5. AF @ FD
a.
b.
c.
d.
[1]
[2]
[1]
[2]
[1]
[2]
[1]
[2]
Reasons
1. Given
2. Addition Property of Equality
3. Segment Addition Postulate
4. Substitution
5. Definition of congruent segments
AB + BF = AF ; FC + CD = FD
AF = FD
AF = FD
AB + BF = FC + CD
AB = CD; BF = FC
AB + BF = FC + CD
AB + BF = FC + CD
AB + BF = AF ;FC + CD = FD
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