Download Unit 4/BA #1 Review BEGIN BA 1 REVIEW

Unit 4/BA #1 Review
BEGIN BA 1 REVIEW
(G5A)
1) The figures below show how many triangles a convex polygon can be divided into from one vertex.
Which of the following equations could be used to find t, the number of triangles a s- sided polygon have if
divided from one vertex?
A t = 8−s
B t = 3s − 10
C t = s+2
D t = s−2
(G3E)
2) Which of the following shows a valid deductive argument.
A If a point is a midpoint, then it lies in the middle of a segment.
If a point lies the middle of a segment, then it is a midpoint.
Point A is a midpoint; therefore it lies in the middle of the segment.
B If a point is a midpoint, then it divides a segment into two congruent parts.
If a line is a bisector, then it divides a segment into two congruent parts.
Point A lies on a bisector; therefore point A is the midpoint.
C If a point is a midpoint, then it bisects a segment.
If a point bisects a segment, then it lies on a segment bisector.
Point A is a midpoint; therefore point A lies on a segment bisector.
D If a point is a midpoint, then it is between two endpoints.
If a point is between two endpoints, then there are two segments to form a larger segment.
If two segments form a larger segment, then the point between two endpoints is a midpoint.
3) For all values where x > y , then
A x = −4 and y = 2
C x = 9 and y = 3
x
> 0 . Which of the following is a valid counter example?
y
B x = −2 and y = −4
D x = 3 and y = −9
(G3C)
(G3D)
4) Angelica was studying the diagrams below to develop a conjecture about the segments contained on
segment AD. ( AD )
A
12 cm
D
14 in
6 cm
12 cm
C
B
5 in
14 in
Which of the following could Angelica determine from the diagrams?
A AB = CD
B AB = BC
C BC = CD
18 mm
6 mm
18 mm
D AB + CD = AD
(G4A)
5) IF AB
A
intersecting with DE at point C, which of the following best illustrates the situation?
B
D
C
C
B
B
A
A
E
E
D
D
C
D
C
D
B
C
A
A
B
E
E
(G3C)
T
6) Given: MS , m5 = 47°
Prove: m 6 = 133°
Statements
1.
5 & 6 are a Linear Pair
2.
3.
4.
5.
5 & 6 are supp.
m5 + m 6 = 180°
m5 = 47°
47 + m 6 = 180°
6.
m6 = 133°
M
6 5
U
S
Reasons
Definition of Linear
Pair
Linear Pair Theorem
Given
Substitution, steps 2
and 3
Subtraction Property
Which of the following should go in the blank to justify the statement?
A Angle Addition Postulate
B Definition of Supplementary
C Definition of adjacent angles
D Definition of angle bisector
(G3C)
7) Emily’s solution for mMAT in the problem is shown below given that mMAH = 65° .
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
5x + 8 = 6x + 2
8=x+2
6=x
mMAT = 5(6) – 3
mMAT = 27°
M
T
(5x + 8)°
A
In which step, if any was an error introduced?
A There is no error
B Step 1
(6x + 2)°
C Step 2
H
D Step 4
(G2B)
8) Students were asked to make conjectures about the figure. Some student responses are below.
A
E
I
II
B
F
D
C
H
Plane ABC intersects plane EDB at point B.
Plane BDH intersects every other plane in the figure
III HG is the intersection of plane EFH and plane GHD
IV C is the intersection of 3 planes
G
Which of the conjectures are correct?
A I and III only
B II and IV only
C II, III and IV only
D None are correct
(G4A)
9) ABC is bisected by BD . If mDBC = (6 x + 3)° and mABC = (13 x − 1)° , which of the following is
true?
A ABD and DBC are supplementary
C ABC and DBC are supplementary
B ABD and DBC are complementary
D ABC and DBC are complementary
(G3E)
10) Given: If an angle’s measure is 90°, then it is a right angle.
If an angle is a right angle, then it is not obtuse.
Conjecture: If m<A = 90°, ___________
Which would complete the conjecture with a valid conclusion using deductive reasoning?
A then it is a right angle
B then it is not obtuse
C then it measures 90°
D then it is not acute
(G7B)
20) The line y = ¼x – 4 is drawn on a coordinate grid. A second line is drawn with a slope of –¾.
Which statement best describes the relationship between these two graphs?
A The second line is less steep than the first line.
C The two lines are oblique and perpendicular.
B The graphs are of intersecting lines.
D The graph of the two lines do not intersect.
(G7C)
21) Which equation is perpendicular to a line containing the points (2, -5) and (4, 5)?
A 5y + x = 10
B
y = ¼x + 13
C y = -4x + 9
D x – 5y = -8
22)
(G7B)
Mr. Porter has two linear functions written on the board: y = ¼x – 3 and 2x – 4y = 12. He wants to
determine whether these linear functions are parallel, perpendicular or oblique. Which procedure below
could he use to find his answer?
A
B
C
D
Change y = ¼x – 3 into standard form to compare the y-intercept.
Look at both “m” after changing 2x – 4y = 12 into slope-intercept form.
Change 2x – 4y = 12 into point-slope form.
Plug in values for y = ¼x – 3 and see if it makes parallel lines.
(G7B)
23) Graph the three points A(1,1), B(4,4), C(6,2).
Which of the following could you use to prove that the shaped formed is a right triangle?
A Slope of AC is ⊥ to the slope of BC
B
Slope of AB is to the slope of BC
C Slope of AC is to the slope of BC
D
Slope of AB is ⊥ to the slope of BC
(G2A)
24) Given the construction below, which of the following is not a valid conclusion?
A
B
C
D
WX = WY
WV ≠ VZ
WV ⊥ XY
∆WVX and ∆WVY are congruent right triangles.
V
(G7C)
25) Charlie was on a hiking trip and was using a GPS system to measure how far he would go. If at the start
of a trip the GPS says his location was at (114.67, 57.9) and at the end of his hike the GPS says he was
at location (108.68, 49.9). How far, in miles, did Charlie travel on his trip?
(G7C)
26) What is the length of AB?
A 1
B
2
C 2 7
D 7 2
(G3E)
27) Finish the statement to form a valid conclusion using deductive reasoning.
Given: If two lines are perpendicular, then their slopes are opposite reciprocals.
If two lines have slopes that are opposite reciporcals, then the product of their slopes is -1.
A If AB
B If AB
⊥ PQ , then the two lines are perpendicular.
⊥ PQ , then the product of their slopes is -1.
C If AB ⊥ PQ , then their slopes are opposite reciprocals.
D Not enough information to make a conclusion.
28) Euclidean Geometry is the study of flat space. Non-Euclidean Geometry includes the study of spherical
geometry. Following are two facts found in Non-Euclidean geometry:
In curved space, the sum of the angles of any triangle is now always greater than 180°
On a sphere, there are no straight lines. As soon as you start to draw a straight line, it curves on the
sphere.
•
•
Which of the following statements is valid within Non-Euclidean Geometry?
I. Given triangle ABC, the sum of <A+<B+<C = 180
II. If two lines are parallel, they never intersect.
A. Statement I
B. Statement II
C. Statement I and II
D. Neither statement is valid
29) The diagram at the right is a construction involving <ABC. Which of the following statements is NOT
true?
a. m<ABD + m<CBD = m<ABC
b. m<ABD = ½ m<ABC
c. m<DBC = m<ABC
d. m<ABC = 2(m<CBD)
30) Which pairs of statements are logically equivalent?
I. If two angles are vertical, then they are congruent.
If two angles are congruent, then they are vertical.
II. If you have a square, then you have a rectangle.
If you do not have a rectangle, then you do not have a square.
III. If all three sides of a triangle are equal, then all three angles are equal.
If the three angles of a triangle are not congruent, then it is not equilateral.
A.
B.
C.
D.
I, II, and III
I and III
II and III
I and II
31) What is the inverse of the statement?
If a polygon is regular, then it is convex.
A.
B.
C.
D.
If a polygon is not regular, then it is not convex.
If a polygon is convex, then it is regular.
If a polygon is not regular, then it is convex.
If a polygon is not convex, then it is not regular.
32) The diagram below illustrates the construction of PS parallel to RQ through point P.
Which statement justifies this construction?
a. m<1 = m<2
c. PR ≅ RQ
b. m<1 = m<3
d. PS ≅ RQ
33) Two lines in a plane always intersect in exactly one point. Which of the following best describes a
counterexample in the assertion above?
A Coplanar lines
B Parallel lines
C Perpendicular lines
D Intersecting lines
34) Line n intersects lines p, q, r, and s, forming the indicated angles.
Which two lines are parallel?
a. q and r
b. p and r
c. r and s
d. p and q
n
130°
p
40°
q
r
50°
s
35°
35) Two lines are intersected by a transversal so that ∠1 and ∠2 are corresponding angles, ∠1 and ∠3 are
alternate exterior angles, and ∠3 and ∠4 are corresponding angles.
If ∠2 ≅ ∠4 , then by what theorem or postulate can be used to prove the lines parallel?
A. Converse of the Corresponding ∠ ' s Theorem.
B. Converse of the Alternate Interior ∠ ' s Theorem.
C. Alternate Exterior ∠ ' s Theorem
D. Same Side Interior ∠ ' s Theorem