Geometry – Fall Midterm Form A

Geometry – Fall Midterm Form A
Distance
1. A civil engineer is drawing a plan for the location and
length of a new underground sewer pipe on a
coordinate grid. The pipe on the plan will run from
point 𝑁 (𝑎, −2) to point 𝑃(1, 𝑏) on the coordinate
grid. Which expression represents the shortest
distance between 𝑁 and 𝑃 in units?
A.
2
2
2
2
(𝑎 + 2) + (1 − 𝑏)
B.
(1 − 𝑎) + (b + 2)
C.
√(𝑎 + 2)2 + (1 − 𝑏)2
D.
√(1 − 𝑎)2 + (𝑏 + 2)2
2. ̅̅̅̅
𝐶𝐷 has an endpoint at (2, −1) and a midpoint at
̅̅̅̅ ?
(8, 3). Which measure is closest to the length of 𝐶𝐷
Midpoint
4. Find the midpoint of the segment with endpoints
(−2, 4) and (4, −5)
7
)
2
A. (−3,
B. (−6, −7)
C. (1,
1
)
2
1
2
D. (1, − )
5.
A. 20.4 units
The coordinate of the midpoint of a segment is
(3, 4) and the coordinate of one endpoint is
(−2, 8). What is the coordinate of the other
endpoint?
B. 8.9 units
A. (−7, 12)
C. 14.1 units
B. (−6, 2)
D. 11.7 units
C. (4, −6)
D. (8, 0)
3.
Bill placed a coordinate grid over a drawing of his
backyard. Points A (-4, -3) and B (4, 7) represent
two corners of his garden. He wants to place a
water sprinkler at the midpoint between A and B.
What is the approximate distance between the
sprinkler and one of the corners of Bill’s backyard?
A. 1.25 units
B. 6.40 units
C. 12.81 units
D. 20.5 units
6.
If 𝐴𝐵 = 𝐵𝐶, use the information below to
determine 𝐴𝐶
A.
5
B.
9
C.
35
D.
70
Geometry – Fall Midterm Form A
10. Solve for the measure of angle 𝐴𝐸𝐶
Geometric Figures
7.
Find the measure of ∠QRT.
T
(3𝑥 + 5)𝑜
(10𝑥 − 7)𝑜
R
Q
S
Record your answer and fill in the bubbles on the
answer document.
8.
Point A is located at (8, 6) and point B is located at
(-3, 0). Point C is between points A and B such that
AC = ¼ AB. What are the coordinates of point C?
1 3
4 2
A. (− , )
5 3
4 2
B. ( , )
C. (5, 6)
D. (
9.
21 9
, )
4 2
In the figure below, ̅̅̅̅̅
𝑊𝑌 bisects VWZ,
m VWY=32, and m VWX=117. What is the
m∠ ZWX?
A.
27
B.
54
C.
108
D.
128
Conditional Statements
11. A statement is given below.
The number of square units in the area of a
square is greater than or equal to the number
of units in the perimeter of the square.
Which side length of a square provides a
counterexample to the given statement?
A. 6 units
B. 4 units
C. 10 units
D. 2 units
12. What is the inverse of the statement in the box?
If a polygon is regular, then it is convex.
A.
85
B.
53
C.
42.5
D.
26.5
A. If a polygon is not regular, then it is not
convex.
B. If a polygon is convex, then it is regular.
C. If a polygon is not regular, then it is convex.
D. If a polygon is not convex, then it is not
regular.
Geometry – Fall Midterm Form A
13. Which set of statements represents a valid
deductive argument?
A. All quadrilaterals have 4 angles.
All parallelograms have 4 angles.
All quadrilaterals are parallelograms.
16. Select the correct converse of the statement, “If an
animal can swim, then it is a fish.”
B. All parallelograms have diagonals that
bisect each other.
All parallelograms have opposite sides that
are parallel.
All polygons whose diagonals bisect each
other have opposite sides that are parallel.
A. If an animal can swim, then it is a fish.
B. If an animal is a fish, then it can swim.
C. If an animal is not a fish, then it cannot swim.
D. If an animal cannot swim, then it is not a fish.
Proofs
17. Given ∆𝐴𝐵𝐶 is a right triangle with 𝑚 𝐴 = 90°.
C. All rectangles have 4 right angles.
All squares have 4 right angles.
All rectangles are squares.
D. All parallelograms have 4 sides.
All polygons with 4 sides are quadrilaterals.
All parallelograms are quadrilaterals.
14. What is the contrapositive of the statement below?
“If today is Friday, then tomorrow is Saturday.”
A.
If tomorrow is not Saturday, then today is not
Friday.
B.
If today is Saturday, then tomorrow is not
Friday.
C.
If tomorrow is Saturday, then today is Friday.
D.
If today is not Friday, then tomorrow is not
Saturday.
15. The conditional statement “If m A=99⁰, then
is obtuse” is true. Which of the following
statements must also be true?
I.
II.
III.
Prove: B and C are complementary. Supply
the missing reason in the proof below.
Statements
𝑚 𝐴 + 𝑚 𝐵 + 𝑚 𝐶 = 180°
Reasons
Triangle Sum
Theorem
𝑚 𝐴 = 90°
Given
90° + 𝑚 𝐵 + 𝑚 𝐶 = 180°
Substitution
𝑚 𝐵 + 𝑚 𝐶 = 90°
Subtraction
𝐵 𝑎𝑛𝑑 𝐶 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
????
A.
Definition of supplementary angles
B.
Angle addition postulate
C.
Substitution
D.
Definition of complementary angles
18. What is the reason for Step 4 in the proof?
Given
Prove
1 ≌
2 ≌
4
3
A
If A is obtuse, then m A = 99⁰
If A is not obtuse, then m A ≠ 99⁰
If m A ≠ 99⁰, then A is not obtuse.
A.
I and II only
B.
II and III only
C.
II only
D.
III only
A.
B.
C.
D.
Vertical Angle Congruence Theorem (Thm. 2.6)
Given
Transitive Property of Congruence (Thm. 2.2)
Symmetric Property of Congruence (Thm. 2.2)
Geometry – Fall Midterm Form A
19. State the property that justifies the following
statement: If 𝑚 1 = 25 and 𝑚 2 = 25, then
𝑚 1= 𝑚 2
A.
B.
C.
D.
22.
is graphed on the coordinate grid below.
Reflexive Property
Substitution Property
Transitive Property
Symmetric Property
20. State the reason for step 7.
Which of the following equations best represents
the perpendicular bisector of
?
A. 𝑦 =
Given: 𝑚∠𝐴𝐶𝐵 = (5𝑥)° and 𝑚∠𝐵𝐶𝐸 = (9𝑥 + 40)°
Prove: 𝑚∠𝐴𝐶𝐷 = 130°
Statement
Reason
1. 𝑚 𝐴𝐶𝐵 + 𝑚 𝐵𝐶𝐸 = 180
2. 5𝑥 + 9𝑥 + 40 = 180
1. ?
2. ?
3. 14𝑥 + 40 = 180
3. Combine Like Terms
4. 14𝑥 = 140
4. ?
5. 𝑥 = 10
5.
6.
7.
8.
7.
8.
6.
7.
8.
9.
8.
𝑚 𝐵𝐶𝐸 = 9𝑥 + 40
𝑚 𝐵𝐶𝐸 = 90 + 40
𝑚 𝐵𝐶𝐸 = 130°
𝐵𝐶𝐸 ⩭
𝐴𝐶𝐷
𝑚∠𝐴𝐶𝐷 = 130°
Division Property of Equality
Given
1
3
𝑥−2
B. 𝑦 = −3𝑥 + 8
C. 𝑦 = 3𝑥 − 10
1
3
D. 𝑦 = − 𝑥 + 1
23. The slopes of the sides of quadrilateral ABCD are
shown in the table below.
Substitution
Combine like terms
?
Substitution Property
Side
̅̅̅̅
𝐴𝐵
̅̅̅̅
𝐵𝐶
A.
B.
C.
D.
Vertical Angles Congruence Theorem
Linear Pair Postulate
Segment Addition Postulate
Substitution Property of Equality
Lines
21. The graph of line 𝑔 is shown below.
Which equation describes a
line parallel to 𝑔 that has a
𝑦 −intercept at (0, -1)?
A.
𝑦 = 2𝑥 − 1
B.
𝑦 = 𝑥−1
C.
𝑦 =− 𝑥−1
D.
𝑦 = −2𝑥 − 1
1
2
1
2
̅̅̅̅
𝐶𝐷
̅̅̅̅
𝐴𝐷
Slope
2
5
5
−
2
2
5
5
−
2
Which statement describes the relationship
between the sides of the quadrilateral?
Geometry – Fall Midterm Form A
24. In rectangle ABCD, the slope of
the slope of
?
is
1
.
2
What is
27. Which of the following statements prove that 𝑎║𝑏?
A. −2
B.
C.
−1
2
1
2
I.
II.
III.
D. 2
Angles
25. A carpenter is making parallel cuts on a piece of
wood as shown below. The long edges of the
board,
are parallel to each other.
A.
B.
C.
D.
∠1 ≌ ∠4
∠2 ≌ ∠7
∠6 ≌ ∠3
III only
I and II only
II and III only
I, II, and III
Use this figure for Items 28-29.
If
A. 140⁰
B. 40⁰
C. 180⁰
D. 70⁰
26. What value of 𝑥 proves that 𝑚║𝑛?
28. If 𝑙║𝑚, 𝑚∠4 = 12𝑥 + 5, and 𝑚∠5 = 8𝑥 + 17, then
what is 𝑚∠2?
A. 139⁰
B. 7.9⁰
C. 3⁰
Record your answer and fill in the bubbles on the
answer document.
D. 41⁰
29. If 𝑙║𝑚, which two angles are supplementary?
A. ∠1 and ∠6
B. ∠3 and ∠5
C. ∠1 and ∠8
D. ∠4 and ∠5
Geometry – Fall Midterm Form A
ANSWER KEY
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
Answer
Distance
D
C
B
Midpoint
D
D
D
Geometric Figures
47o
D
B
D
Conditional Statements
D
A
D
A
C
B
Proofs
D
A
B
A
Lines
C
A
B
C
Angles
A
141
C
D
B
TEK
G.2B
G.2B
G.2B
G.2B
G.2B
G.5B
G.6A
G.2A
G.6A
G.6A
G.4C
G.4B
G.4A
G.4B
G.4B
G.4B
G.6A
G.6A
G.6A
G.6A
G.2C
G.2C
G.2B
G.2B
G.5A
G.6A
G.6A
G.5A
G.5A