Download GEOMETRY EXAM 1.1 1. Jason designed a mall entrance made of

GEOMETRY EXAM 1.1
1. Jason designed a mall entrance made of wrought iron. The wrought iron used to make the 16 line
segments between the two concentric circles are each 1.5 m long. Find the total length of
wrought iron used to make the structure. Round the answer to the nearest meter. (3 points)
2. Find the volume of the composite space figure to the nearest whole number.
(3 points)
3. Which biconditional is NOT a good definition?
A. A whole number is odd if and only if the number is not divisible by 2.
B. An angle is straight if and only if its measure is 180.
C. A whole number is even if and only if it is divisible by 2.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.
(1 point)
4. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, state not
possible.
(1 point)
Statement 1: If two lines intersect, then they are not parallel.
Statement 2:
do not intersect.
For questions 5-7, create a simple deductive argument of the given form. Use a Venn diagram to illustrate
whether or not the argument is valid and/or sound.
(3 points each)
5. Affirming the conclusion
6. Denying the hypothesis
7. A chain of conditionals
8. Write an equation of the line through point S(–10, –3) and perpendicular to the line with equation
-4x + 7y = -28.
(2 points)
9. Which two lines are parallel?
(1 point)
I.
II.
III.
A. I and II
C. II and III
B. I and III
D. No two of the lines are parallel.
____ 10. Complete the statement. If a transversal intersects two parallel lines, then ____.
(1 point)
A. corresponding angles are supplementary
B. same-side interior angles are complementary
C. alternate interior angles are congruent
D. none of these
____ 11. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary.
A. Acute
C. same-side interior
B. alternate interior
D. Corresponding
( 1 point)
12. In the figure below, which lines, if any, can you conclude are parallel given that
?
Justify your conclusion with a theorem or postulate.
(1 point)
g
1
j
2
h
k
A.
, by the Converse of the Same-Side Interior Angles Theorem
B.
, by the Converse of the Alternate Interior Angles Theorem
C.
, by the Converse of the Alternate Interior Angles Theorem
D.
, by the Converse of the Same-Side Interior Angles Theorem
13. Find the values of x and y. The diagram is not to scale.
(x – 3)°
41°
(y + 8)°
74°
(2 points)
14. Find
The diagram is not to scale.
Q
(1 point)
R
70°
50°
15. Complete the two-column proof.
Given:
are supplementary.
Prove:
(3 points)
16. You are given that 2c2 = 2bc + ac with c ≠ 0. Justify each step of the proof that 4b = 4c – a. (2 points)
2
2c2 = 2bc + ac
a. Given
2
b.
4c2 = 4bc + ac
4c = 4b + a
c.
4c – a = 4b
d.
4b = 4c – a
e.
For Questions 17-18 use the diagram below. Suppose m 1 = 3x + 10, m 2 = 3x + 14, and m 6 = x + 58.
17. Find the value of x for which a || b.
18. Find the value of x for which m || n.
(2 points)
(2 points)
19.
(1 point)
What can you conclude from the information in the diagram?
A. 1.
2.
3.
B. 1.
2.
3.
C. 1.
2.
3.
D. 1.
2.
3.
are vertical angles
are adjacent angles
is a right angle
are vertical angles
is a right angle
are adjacent angles
20.
In the figure shown,
. Which of the following statements is false?
(1 point)
Not drawn to scale
A.
B.
C.
D.
21.
BEC and CED are adjacent angles.
AED and BEC are adjacent angles.
How are the two angles related?
(1 point)
52°
128°
Drawing not to scale
A. Vertical
B. Supplementary
and
C. complementary
D. adjacent
22.
If
are supplementary angles and
23.
What is a correct name for the polygon?
, find
and
(1 point)
(1 point)
A
B
E
C
D
A. EDCAB
B. ABCDA
C. CDEAB
D. BAEAB
24.
25.
Which figure is a convex polygon?
A.
C.
B.
D.
Find the distance between the parallel lines:
y=x–6
y=x+8
a.
b.
(1 point)
(4 points)