Geometry 2017 Exam DOES NOT REQUIRE MATH
80 m
A midsegment of a triangle measures 40 m. What is the length of the corresponding base of the triangle? A) 20 m B) 40 m C) 60 m D) 80 m
x = 24 and y = 13
For what value of x and y is the following quadrilateral a parallelogram? A) x = 13 and y = 13 B) x = 24 and y = 24 C) x = 13 and y = 24 D) x = 24 and y = 13
8
For what value of x is the following quadrilateral a parallelogram? A) 5 B) 8 C) 10 D) 13
105
For what value of x is the following quadrilateral a parallelogram? A) 75 B) 95 C) 105 D) 115
x = 60 and y = 120
For what values of x and y is the following quadrilateral a parallelogram? A) x = 120 and y = 60 B) x = 60 and y = 120 C) x = 60 and y = 60 D) x = 90 and y = 90
m∠1< m∠2
If AB = 5 and BC = 6, which of the following most accurately describes the figure? A) m∠1< m∠2 B) m∠1 ≤ m∠2 C) m∠1 ≥ m∠2 D) m∠1> m∠2
BC<CD
If AB≅AD, what can we conclude from the figure? A) BC<CD B) BC≤CD C) AB⊥BC D) ∆ABC~ ∆ADC
orthocenter.
The point at which all three altitudes of a triangle intersect is called the A) orthocenter. B) centroid. C) base. D) altitude.
6
There are 24 offices in a building that contains 4 floors. On average, how many offices are on each floor?
(5, 3)
What are the coordinates of the undefined vertex in the parallelogram below? A) (1, 5) B) (3, 5) C) (4, 3) D) (5, 3)
false, true, true, false
What are the values, from top to bottom, that complete the last column in the truth table? A) false, true, true, false B) true, true, true, false C) true, true, false, false D) true, false, false, true
24°
If ∆ABC≅∆DEF, what is the measure of ∠F? A) 78° B) 24° C) 36° D) 42°
6 cm
If ∆ABC≅∆DEF,what is the length of line segment DF? A) 4 cm B) 6 cm C) 8 cm D) 10 cm
80°
If ∆JKL≅∆WXY, what is the measure of ∠W? A) 100° B) 40° C) 20° D) 80°
line segment DE≅ line segment JK
In order for ∆DEF to be congruent to ∆JKL by ASA, what else needs to be true in the figure below? A) line segment DE≅ line segment JK B) ∠F≅∠L C) Line segment DF≅ line segment JL D) line segment FE≅ line segment LK
m∠BAC > m∠CED
What can we conclude from the figure below? A) AB‖DE B) m∠BAC > m∠CED C) AC > CE D) AC ≥ CE
that two triangles are similar
What is the Hinge Theorem Converse used to show? A) that two triangles are similar B) the relative lengths of the corresponding sides in two triangles C) the congruency of adjacent sides D) the relative measures of the corresponding angles in two triangles
the relative lengths of the corresponding sides in two triangles
What is the Hinge Theorem used to show? A) that two triangles are similar B) the relative lengths of the corresponding sides in two triangles C) the congruency of adjacent sides D) the relative measures of the corresponding angles in two triangles
∆XZY≅∆TSU
What is the correct way to name these congruent triangles? A) ∆XYZ≅∆UTS B) ∆ZXY≅∆UST C) ∆YZX≅∆TSU D) ∆XZY≅∆TSU
∆ CAB ~ ∆DFE
What is the correct way to state that the triangles below are similar? A) ∆ ABC ~ ∆DEF B) ∆ CAB ~ ∆DFE C) ∆ CBA ~ ∆DFE D) ∆ BAC ~ ∆FED
0
What is the slope of the line that contains the points (-6, -2) and (3, -2)? A) -³/₄ B) 0 C) ⁴/₉ D) The slope is undefined.
The slope is undefined.
What is the slope of this line? A) 0 B) 2 C) -2 D) The slope is undefined.
0
What is the slope of this line? A) 1 B) 0 C) 3 D) The slope is undefined.
-3
What is the slope of this line? A) -3 B) 3 C) ¹/₃ D) - ¹/₃
The slope is undefined.
What is the slope of this line? A) -4 B) 0 C) 1 D) The slope is undefined.
0
What is the slope of this line? A) -4 B) 0 C) ¼ D) The slope is undefined.
²/₃
What is the slope of this line? A) ²/₃ B) ³/₂ C) 2 D) The slope is undefined.
AB = 25 and BC = 20
What should the lengths of AB and BC be for the figure to be a parallelogram? A) AB = 20 and BC = 25 B) AB = 20 and BC = 20 C) AB = 25 and BC = 20 D) AB = 25 and BC = 25
y = ²/₇ x +1
Which choice is the equation of a line that passes through point (7, 3) and is parallel to the line represented by this equation? y = ²/₇ x -3 A) 7x + 3y = 2 B) y = ²/₇ x +1 C) y = - ⁷/₂ x -3 D) 2x + 7y = 1
∠U≅∠X
In order for ∆TUV to be congruent to ∆WXY by AAS, what else needs to be true in the figure below? A) ∠V≅∠Y B) ∠U≅∠X C) line segment UT ≅ line segment WX D) line segment UV ≅ line segment XY
EB
In the following figure, which segment is a median of ∆ABC? A) AC B) GF C) CG D) EB
A
Which choice is the graph of a line parallel to the line represented by this equation? y=²/₃x+2
C)
Which choice is the graph of a line that is perpendicular to the line represented by this equation? y = 3
C)
Which choice is the graph of a line that is perpendicular to the line represented by this equation? y = −2x + 7
right angles
Which description does not apply to the figure given below? A) linear pair B) right angles C) adjacent angles D) supplementary angles
A, D, G, and F
Which four points are NOT coplanar in the box pictured below? A) D, C, G, and F B) A, H, D, and B C) A, D, G, and F D) C, I, F, and E
∆ABC ~ ∆DFE
Which is the most accurate statement about the two triangles below? A) ∆ABC ~ ∆DEF B) ∆ABC ~ ∆DFE C) ∆ABC ≅ ∆DFE D) none of the above
∆ABE ~ ∆DBC
Which is the most accurate statement about the two triangles below? A)∆AEB ~ ∆DBC B) ∆ABE ~ ∆DBC C) ∆ABC ~ ∆BCD D) none of the above
BC < EF
Which is the most accurate statement about these two triangles? A) EF > BC B) ∆BAC ~ ∆EDF C) DE > DF D) BC < EF
∠3
Which of the following angles is NOT congruent to ∠6? A) ∠ 8 B) ∠ 4 C) ∠3 D) ∠2
B)
Which of the following figures is a parallelogram?
a kite
Which of the following is NOT a parallelogram? A) a rhombus B) a kite C) a rectangle D) a square
Adjacent sides have to be congruent.
Which of the following is NOT true of a parallelogram? A) Opposite sides have to be congruent. B) Opposite sides have to be parallel. C) Adjacent sides have to be congruent. D) Opposite angles have to be congruent.
Transitive Property of Equality
Which of the following justifies the statement below? A) Substitution Property of Equality B) Complement Theorem C) Addition Property of Equality D) Transitive Property of Equality
Transitive Property of Equality
Which of the following justifies the statement below? If AB = BC and BC = DE, then AB = DE. A) Transitive Property of Equality B) Segment Addition Postulate C) Distributive Property of Equality D) Symmetric Property of Equality
B)
Which of the following quadrilaterals is NOT a parallelogram?
B)
Which of the following quadrilaterals is a parallelogram?
10.5 in.
The base of a triangle measures 21 in. What is the measure of the corresponding midsegment of the triangle? A) 7 in. B) 10.5 in. C) 21 in. D) 42 in.
Complementary angles
_____ are two angles whose measures sum to 90°. A) Supplementary angles B) Adjacent angles C) Complementary angles D) Acute angles
Side-Angle-Side Similarity
A) Angle-Angle Similarity B) Side-Side Similarity C) Side-Angle-Side Similarity D) Angle-Side-Angle Similarity
18 in.
AD, BE, and CF are medians of ∆ABC. Given that CG = 36 in., find GF. A) 9 in. B) 12 in. C) 18 in. D) 24 in.
always
Any three points are _____ coplanar. A) never B) always C) occasionally D) frequently
point B
At which point do plane ABCD and line segment BE intersect? A) point A B) point B C) point C D) point E
∠1≅∠2
Because corresponding angles are congruent, which two angles in the figure below are congruent? A) ∠1≅∠2 B) ∠1≅∠3 C) ∠2≅∠3 D) lines m and n are parallel
always true
Determine whether the following statement is always, sometimes, or never true. Two angles that form a linear pair are supplementary. A) always true B) sometimes true C) never true D) There is not enough information to determine this.
5 ft
ED is a midsegment of ∆ABC . What is the length of DB? A) 5 ft B) 6 ft C) 8 ft D) 10 ft
10 in.
ED is a midsegment of ∆ABC. If ∆ABC is equilateral, what is the length of AD? A) 6 in. B) 8 in. C) 10 in. D) 12 in.
12 cm
ED is a midsegment of ∆ABC. What is the length of BC? A) 10 cm B) 12 cm C) 14 cm D) 18 cm
BC
G is the centroid of ∆ABC. Which segment is an altitude of the triangle? A) BC B) AB C) CD D) AE
∆ABE ~ ∆DBC
Given that AB/BD = BE/BC, which statement is true? A) ∆AEB ≅ ∆CDB B) ∆ABE ~ ∆DCB C) ∆ABE ~ ∆DBC D) ∆ABE ≅ ∆DCB
m∠BAC≥ m∠EDF
Given that BC ≥EF, which statement is true? A) m∠BAC< m∠EDF B) m∠BAC≤ m∠EDF C) m∠BAC≥ m∠EDF D) m∠BAC> m∠EDF
(x+y)>z
Given that x, y, and z are the lengths of the sides of a triangle, and that x<y<z , which of the following is true? A) (x+y)>z B) (y-z)>x C) (y-x)>z D) (x+y)=z
Angle-Angle Similarity
Given that ∠AEB ≅ ∠BCD, which of the following can be used to show that ∆ABE ~ ∆DBC ? A) Angle-Angle Similarity B) Side-Side Similarity C) Side-Angle-Side Similarity D) Angle-Side-Angle Similarity
CD ≥ BC
If m ∠1 ≤ m∠2, which of the following most accurately describes the figure? A) CD > BC B) CD ≥ BC C) BC > CD D) BC ≥ CD
BC>CD
If m∠1>m∠2, which of the following most accurately describes the figure? A) BC≅CD B) BC<CD C) BC>CD D) BC≥CD
similar
If the corresponding angles of two triangles are congruent, then the two triangles are _____. A) congruent B) equal C) mirror images D) similar
No, there is not enough information.
Line segment AB≅ line segment DE and C is the midpoint of line segment AE. Is there enough information in the figure below to prove that ∆ACB≅∆ECD? A)Yes, by ASA, because ∠A≅∠E, line segment AC≅ line segment EC, and ∠ACB≅∠ECD B) Yes, by SSS, because line segment AB ≅ line segment DE, line segment AC ≅ line segment EC, and line segment BC ≅ line segment DC. C) Yes, by AAS, because ∠A≅∠E, ∠ACB≅∠ECD, and line segment BC ≅ line segment DC. D) No, there is not enough information.
5 m
MN is a midsegment of ∆JKL. What is the length of MN ? A) 4 m B) 5 m C) 6 m D) 8 m
congruent corresponding angles
Similar triangles have _______. A) congruent corresponding angles B) one vertical pair C) congruent corresponding sides D) parallel opposing sides
Pythagorean Theorem
The Distance Formula is based on which theorem? A) Pythagorean Theorem B) Complement Theorem C) Perpendicular to Parallels Theorem D) Equipartition Theorem
Side-Side-Side Inequality Theorem
The Hinge Theorem Converse is based on the _____. A) Angle-Angle-Side Inequality Theorem B) Side-Angle-Side Inequality Theorem C) Side-Side-Angle Inequality Theorem D) Side-Side-Side Inequality Theorem
Side-Angle-Side Inequality Theorem
The Hinge Theorem is based on the _____. A) Angle-Angle-Side Inequality Theorem B) Side-Angle-Side Inequality Theorem C) Side-Side-Angle Inequality Theorem D) Side-Side-Side Inequality Theorem
sum
The Triangle Inequality Theorem states that the _____ of the measures of any two sides of a triangle is greater than the measure of the third side. A) difference B) product C) ratio D) sum
a quadrilateral, a parallelogram, and a rhombus.
The following figure is A) a quadrilateral, a square, and a rhombus. B) a quadrilateral, a parallelogram, and a trapezoid. C) a quadrilateral, a trapezoid, and a rhombus. D) a quadrilateral, a parallelogram, and a rhombus.
∠LMN≅∠PMR - vertical angles are congruent
What statement is needed to prove that ∆LMN≅∆PMR by ASA? A) ∠L≅∠P - alternate interior angles are congruent B) Line segment LM≅ line segment PM - definition of midpoint C) ∠LMN≅∠PMR - vertical angles are congruent D) Line segment LN ≅ line segment PR - definition of bisector
a quadrilateral with opposite sides that are congruent
Which choice best describes a parallelogram? A) a quadrilateral with congruent sides B) a quadrilateral with opposite sides that are congruent C) a quadrilateral with diagonals that intersect at 90° angles D) a quadrilateral with one pair of adjacent congruent angles
all of the above
Which choice describes a parallelogram? A) a quadrilateral where both pairs of opposite angles are congruent B) a quadrilateral where both pairs of opposite sides are congruent C) a quadrilateral where the diagonals bisect each other. D) all of the above
a quadrilateral where both pairs of opposite sides are parallel
Which choice describes a parallelogram? A) a quadrilateral with diagonals that are congruent B) a quadrilateral with a pair of adjacent congruent angles C) a quadrilateral where both pairs of opposite sides are parallel D) all of the above
a quadrilateral where the diagonals bisect each other
Which choice describes a parallelogram? A) a quadrilateral with diagonals that are congruent B) a quadrilateral with a pair of adjacent congruent angles C) a quadrilateral where the diagonals bisect each other D) all of the above
a quadrilateral with congruent diagonals
Which choice does NOT describe a parallelogram? A) a quadrilateral where both pairs of opposite sides are congruent B) a quadrilateral with congruent diagonals C) a quadrilateral where both pairs of opposite sides are parallel D) a quadrilateral with congruent opposite angles
Two distinct planes can intersect at a point.
Which of the following statements is false? A) Three distinct planes can intersect at a line. B) Two distinct planes can intersect at a point. C) Three distinct planes can intersect at a point. D) Two distinct planes can intersect at a line.
∆ABC≅∆DFE by ASA
Which of the following statements is true? A) ∆ABC≅∆DFE by SSS B) ∆ABC≅∆DFE by AAS C) ∆ABC≅∆DFE by ASA D) ∆ABC≅∆DEF by ASA
∆JKL≅∆PQR by AAS
Which of the following statements is true? A) ∆JKL≅∆PQR by ASA B) ∆JKL≅∆PQR by SAS C) ∆JKL≅∆PQR by SSS D) ∆JKL≅∆PQR by AAS
∠ABC≅∠DCE
Which one of the following cannot be concluded from the figure below? A) AB‖DE B) ∠CED≅∠CAB C) AB≅DE D) ∠ABC≅∠DCE
∆EDF and ∆SRT
Which pair of triangles are congruent by AAS? A) ∆NQP and ∆ABC B) ∆EDF and ∆SRT C) ∆GHJ and ∆ZYX D) ∆NQP and ∆KLM
point B
Which point is collinear with points D and E in the figure below? A) point A B) point H C) point B D) point G
G
Which point is the centroid of ∆ABC? A) A B) F C) G D) D
M
Which point is the orthocenter for ∆JKL? A) J B) A C) C D) M
point E
Which point must be included in the name of the plane below? A) point E B) point A C) point D D) point C
2, 5, 4
Which set of numbers could be the lengths of the sides of a triangle? A) 2, 5, 4 B) 3, 5, 9 C) 4, 9, 3 D) 17, 15, 2
15, 8, 9
Which set of numbers could be the lengths of the sides of a triangle? A) 4, 9, 5 B) 2, 4, 6 C) 8, 3, 2 D) 15, 8, 9
The planes intersect at infinitely many points.
Which statement about the figure below is true? A) Four planes are pictured. B) The planes do not intersect. C) The planes intersect at a point. D) The planes intersect at infinitely many points.
The planes intersect at one point.
Which statement about the figure below is true? A) The planes intersect at one point. B) The planes intersect at infinitely many points. C) The planes do not intersect. D) Two planes are pictured.
CD > BC
Which statement most accurately describes the figure below? A) AB > AD B) AD > DC C) BC > CD D) CD > BC
CD>BC
Which statement most accurately describes the figure below? A) AB>AD B) AD>DC C) BC>CD D) CD>BC
all of the above
Which type of triangle contains its centroid? A) right B) acute C) obtuse D) all of the above
congruent
∆ABC and ∆DEF are _______. A) balanced B) congruent C) equiangular D) equilateral
35
∆ABC≅∆DEF by ASA. What is the value of x? A) 70 B) 40 C) 35 D) 110
15 mm
∆XYZ≅∆PQR. What is the length of line segment PQ? A) 12 mm B) 15 mm C) 8 mm D) 20 mm
8 mm
∆XYZ≅∆PQR. What is the length of line segment RQ? A) 12 mm B) 15 mm C) 20 mm D) 8 mm
70°
∆XYZ≅∆PQR. What is the measure of ∠Y? A) 80° B) 30° C) 70° D) 100°
28
What can you assume will be the 7th term in the list below? 1, 3, 6, 10, 15, . . . A) 21 B) 28 C) 36 D) 45
A) 0000∆∆∆∆ squares x 4
What can you assume will be the next figure in the list below? A) 0000∆∆∆∆ squares x 4 B) C) D)
10,000, 100,000, 1,000,000
What can you assume will be the next three numbers in the list below? 1, 10, 100, 1000, . . . A) 100, 10, 1 B) 1000, 100, 10 C) 10,000, 100,000, 1,000,000 D) 10,000, 100,000, 10,000,000
proof
What is a logical argument in which each statement made is supported by a statement that is accepted as true? A) theorem B) postulate C) proof D) definition
∆KGH ≅∆VWX
What is the correct way to name these congruent triangles? A)∆KHG ≅∆WVX B)∆ GKH ≅∆XWV C) ∆GHK ≅∆WVX D) ∆ KGH ≅∆VWX
Angle 2 is congruent to angle 3
Fill in the blank with the phrase that makes the proof statement true. Lines m and n are parallel. Angle 1 is congruent to angle 2 by the Corresponding Angles Postulate. Angle 1 is congruent to angle 3 because they are vertical angles. _____________ by the Transitive Property. A) Angle 2 is congruent to angle 3 B) Angle 3 is supplementary to angle 1 C) Angle 2 is congruent to angle 1 D) Angle 1 is complementary to angle 2
51°
Given that m∠ABD = 97°, find m∠CBD. A) 44° B) 51° C) 92° D) 136°
69°
Given that m∠RST=111° and ∠XYZ is supplementary to ∠RST what is m ∠XYZ? A) 69° B) 48° C) 42° D) 21°
Yes. Because line segment FH≅ line segment KH, the triangles are congruent by SSS.
H is the midpoint of line segment KF. Is there enough information in the figure to prove that ∆FGH≅∆KMH? A) Yes. Because ∠F≅∠K , the triangles are congruent by SAS. B) Yes. Because∠G≅∠M , the triangles are congruent by SAS. C) Yes. Because line segment FH≅ line segment KH, the triangles are congruent by SSS. D) No. There is not enough information.
infinitely many
How many distinct lines can be drawn through a fixed point? A) zero B) one C) two D) infinitely many
one
How many distinct lines can be drawn through two fixed points? A) zero B) one C) two D) infinitely many
five
How many planes make up the figure below? A) three B) four C) five D) six
A figure that is a rectangle is therefore a quadrilateral.
If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then it is a quadrilateral. Which statement is valid, based on deductive reasoning? A) A figure that is a parallelogram is therefore a rectangle. B) A figure that is a quadrilateral is therefore a rectangle. C) A figure that is a rectangle is therefore a quadrilateral. D) A figure that is a rectangle is therefore a parallelogram.
trapezoid
If a quadrilateral does not have two pairs of opposite sides that are parallel, then it may be a _____. A) parallelogram B) rhombus C) trapezoid D) square E) rectangle
rhombus
If a quadrilateral has four sides that are all equal in measure, then it may be a _____. A) rectangle B) rhombus C) trapezoid D) pentagon
y = - ⁵/₂ x -3
Which choice could be the equation of a line perpendicular to the line represented by this equation? y = ²/₅ x +2 A) y = ²/₅ x -3 B) y = ⁵/₂ x +7 C) y = - ⁵/₂ x -3 D) y = −2x + 5
y = - ³/₂ x -3
Which choice is the equation of a line that has a y-intercept of -3 and is perpendicular to the line represented by this equation? y = ²/₃ x + 1 A) y = ²/₃ x-3 B) y = 3x− 3 C) y = - ³/₂ x -3 D) y = ³/₂ x +3
y = 6x+ 7
Which choice is the equation of a line that has a y-intercept of 7 and is parallel to the line represented by this equation? y = 6x− 5 A) y = 6x+ 7 B) y = 6x− 7 C) y=-¹/₆x+7 D) y=¹/₆x-7
y=¹/₃x
Which choice is the equation of a line that passes through the point (-6, -2) and is perpendicular to the line represented by this equation? y = −3x + 1 A) 3x + y = 1 B) y=¹/₃x C) y = −3x D) −3y = −x + 1
y = x− 6
Which choice is the equation of a line that passes through the point (5, -1) and is perpendicular to the line represented by this equation? y = −x + 5 A) y = x− 6 B) 5x − y = 5 C) y = −x− 1 D) 2x− 5y = −1
y= 2x + 7
Which choice could be the equation of a line parallel to the line represented by this equation? y = 2x− 3 A) y=-½x+4 B) y= 2x + 7 C) y = −2x + 1 D) y=³/₂x-5
y=⁷/₄x+11
Which choice could be the equation of a line parallel to the line represented by this equation? y=⁷/₄x-6 A) y=⁴/₇x-3 B) y=-⁴/₇x-6 C) y=⁷/₄x+11 D) 4x− 7y = −7
x = 5
Which choice could be the equation of a line perpendicular to the line represented by this equation? y = 5 A) y = 4x− 9 B) y = - ¹/₅ x C) y = 5x D) x = 5
y = - ¹/₅ x+5
Which choice could be the equation of a line perpendicular to the line represented by this equation? y = 5x− 2 A) y = - ¹/₅ x+5 B) y = 5x +2 C) y = ¹/₅ x-7 D) y = −5x + 5
A polygon is a nonagon if and only if it has nine sides.
"A nonagon is a nine-sided polygon." If this statement is true, then which of the following statements must also be true? A) A polygon is not a nonagon if and only if it has nine sides. B) A polygon is a nonagon if and only if it does not has nine sides. C) A polygon has 9 sides if and only if it is not a nonogon. D) A polygon is a nonagon if and only if it has nine sides.
A quadrilateral has exactly four congruent sides and four right angles if and only if it is a square.
"A quadrilateral is a square if and only if it has exactly four congruent sides and four right angles." If this statement is true, then which of the following statements must also be true? A) A square has exactly four congruent sides and four right angles if and only if it is a quadrilateral. B) A quadrilateral is not a square if and only if it has exactly four congruent sides and four right angles. C) A quadrilateral does not have exactly four congruent sides and four right angles if and only if it is a square. D) A quadrilateral has exactly four congruent sides and four right angles if and only if it is a square.
It is a pentagon.
"If a convex polygon has five sides, then it is a pentagon." What is the conclusion of this conditional statement? A) It is a pentagon. B) It is not a pentagon. C) A convex polygon has five sides. D) A convex polygon does not have five sides.
If a parallelogram does not have four right angles, then it is not a rectangle.
"If a parallelogram has four right angles, then it is a rectangle." What is the inverse of this conditional statement? A) If a parallelogram has four right angles, then it is a rectangle. B) If a parallelogram does not have four right angles, then it is a rectangle. C) If a parallelogram has four right angles, then it is not a rectangle. D) If a parallelogram does not have four right angles, then it is not a rectangle.
A polygon has seven sides.
"If a polygon has seven sides, then it is a heptagon." What is the hypothesis in this conditional statement? A) It is a heptagon. B) It is not a heptagon. C) A polygon has seven sides. D) A polygon does not have seven sides.
If the integer is divisible by 3, then it is divisible by 6.
"If the integer is divisible by 6, then it is divisible by 3." What is the converse of this conditional statement? A) If the integer is not divisible by 6, then it is not divisible by 3. B) If the integer is not divisible by 6, then it is divisible by 3. C) If the integer is divisible by 6, then it is not divisible by 3. D) If the integer is divisible by 3, then it is divisible by 6.
You live in San Antonio.
"If you live in San Antonio, then you live in Texas." What is the hypothesis in this conditional statement? A) You live in San Antonio. B) You do not live in San Antonio. C) You live in Texas. D) You do not live in Texas.
New Orleans is not in Louisiana.
"New Orleans is in Louisiana." Which of the following is the negation of this statement? A) New Orleans is not a city. B) Louisiana is in New Orleans. C) New Orleans is not in Louisiana. D) None of the above.
If a triangle has side lengths 3, 4, and 5 units, then its area is 6 square units.
If a triangle has sides of lengths 3, 4, and 5 units, then it is a right triangle. All right triangles have an area equal to one half the product of the two smaller side lengths. Which statement is valid, based on deductive reasoning? A) A polygon has an area of 6 square units if it is a triangle. B) A triangle has a perimeter of 12 units if its sides are consecutive integers. C) If a triangle has side lengths 3, 4, and 5 units, then its area is 6 square units. D) If a triangle has side lengths 4, 5, and 6 units, then its area is 10 square units.
∠AED and ∠CEB are supplementary
If line segment AB and line segment CD intersect at E to form ∠AED and ∠CEB, which of the following is NOT a valid conclusion? A) ∠AED and ∠CEB are vertical angles B) ∠AED and ∠CEB are supplementary C) ∠AED ≅ ∠CEB D) m∠AED ≅ m∠CEB
B and F
If the faces of the figure below represent planes, which of the following are a pair of coplanar points? A) A and F B) B and F C) D and E D) B and G
right angles
If two congruent angles form a linear pair, then they are _____. A) right angles B) acute angles C) obtuse angles D) complementary angles
point
If two distinct coplanar lines are not parallel, their intersection is a _____. A) point B) line C) plane D) square
the lines are perpendicular
If two lines intersect and form 4 right angles, then ___________. A) the lines are parallel B) the lines are perpendicular C) the angles are complementary D) the lines are not coplanar
∠E≅∠K
In order for ∆DEF to be congruent to ∆JKL by SAS, what else needs to be true in the figure below? A)∠D≅∠J B)∠F≅∠L C) ∠E≅∠K D) ∠F≅∠J
line segment RS≅ line segment UV
In order for ∆QRS to be congruent to ∆TUV by SSS, what else needs to be true in the figure below? A) ∠T≅∠Q B) line segment RS≅ line segment UV C) ∠V≅∠S D) ∠Q and ∠T are right angles
142°
In the figure below, m∠1 = 38°, what is m∠2? A) 38° B) 52° C) 90° D) 142°
Yes. Because ∠ACB and ∠DCE are congruent vertical angles, the triangles are congruent by SAS.
Is there enough information in the figure below to prove that ∆ACB≅∆DCE ? A) Yes. Because line segment AB ≅ line segment DE, the triangles are congruent by SSS. B) Yes. Because C is the midpoint of line segment AD, the triangles are congruent by SAS. C) Yes. Because ∠ACB and ∠DCE are congruent vertical angles, the triangles are congruent by SAS. D) No. There is not enough information in the figure.
If yesterday was Tuesday, then tomorrow will not be Friday.
Let p: Yesterday was Tuesday.Let q: Tomorrow will be Friday. If this statement is true, then which of the following statements is true? A) If yesterday was Tuesday, then tomorrow will not be Friday. B) If yesterday was not Tuesday, then tomorrow will not be Friday. C) If tomorrow is Friday, then yesterday was Tuesday. D) If yesterday was not Tuesday, then tomorrow will be Friday
Line segment CD≅ Line segment CD - Reflexive Property of Equality
Line segment CD bisects ∠ADB and ∆ADB is an isosceles triangle. What is another true statement that proves that ∆ADC≅∆BDC? A) Line segment AC≅line segment BC - definition of midpoint B) ∠ACD≅∠BCD - all right angles are congruent C)Line segment CD≅ Line segment CD - Reflexive Property of Equality D) There is not enough information to prove the triangles true.
Yes. Because ∠R≅∠V, the triangles are congruent by SAS.
Line segment RS and Line segment UV are parallel and congruent. Line segment RT and VT are congruent. Is there enough information in the figure to prove that ∆RTS≅∆VTU? A) Yes. Because Line segment ST≅ Line segmentUT , the triangles are congruent by SSS. B) Yes. Because ∠R≅∠V, the triangles are congruent by SAS. C) Yes. Because ∠RTS≅∠VTU , the triangles are congruent by SAS. D) No. There is not enough information.
0
The slope of every horizontal line is... A) 0 B) 1 C) ½ D) undefined
undefined
The slope of every vertical line is... A) 0 B) 1 C) D) undefined
∠TVW≅∠UVW - definition of bisector
W is the midpoint of line segment TU and line segment VW ⊥ line segment TU. Which of the following would NOT be in the proof that ∆TWV≅∆UWV? A) Line segment TW ≅ Line segment UW - definition of a midpoint B) ∠TVW≅∠UVW - definition of bisector C) Line segment VW ≅ line segment VW - Reflexive Property of Equality D) ∠TWV≅∠UWV - all right angles are congruent
(1,1)
WXYZ is a rectangle. At which point do the diagonals intersect? A) (-1,-1) B) (1,1) C) (0,0) D) (2,1)
true, false, false, true
What are the values, from top to bottom, that complete the last column in the truth table? A) true, false, false, true B) false, false, true, true C) true, false, true, false D) false, false, false, true
∆RTS≅∆CED
What is the correct way to name these congruent triangles? A) ∆RTS≅ ∆CED B) ∆ TRS≅∆CDE C) ∆ SRT≅∆ECD D) ∆TSR≅∆DCE
Vertical angles are congruent
What is the missing reason in the proof below? A) Vertical angles are congruent B) Transitive Property of Congruence C) Alternate interior angles are congruent D) Supplementary Theorem
-1
What is the slope of this line? A) 1 B) 3 C) -1 D) -3
1
What is the slope of this line? A) 1/3 B) ½ C) 1 D) 2
-¹/₆
What is the slope of this line? A) 4 B) -³/₂ C) -¹/₆ D) The slope is undefined.
-²/₅
What is the slope of this line? A) ⁵/₂ B) 2 C) -²/₅ D) The slope is undefined.
Line segment SQ≅Line segment SQ- Reflexive Property of Equality
What statement and reason would prove that ∆PQS≅∆RQS by SSS? A) Line segment SQ≅Line segment SQ - Transitive Property of Equality B) ∠PQS≅∠RQS - all right angles are congruent C) Line segment SQ≅Line segment SQ - Reflexive Property of Equality D) Q is the midpoint of Line segment PR- definition of midpoint
∠XYZ≅∠VYW - vertical angles are congruent
What statement and reason would prove that ∆XYZ≅∆VYW by SAS? A)line segment XZ≅line segment VW - parallel lines are congruent B) ∠Z≅∠W - alternate interior angles are congruent C)∠X≅∠V - Corresponding Angles Postulate D) ∠XYZ≅∠VYW - vertical angles are congruent
Three points on the same plane are always collinear.
Which of the following statements is false? A) The intersection of two distinct planes is a line. B) The intersection of a line and a plane is a point, assuming the line doesn't lie on the plane. C) Three points on the same plane are always collinear. D) Two points on the same plane are always collinear.
∆ABC≅∆DEF by SSS
Which of the following statements is true based on the figure below? A)∆ABC≅∆DEF by SSS B) ∆ABC≅∆DEF by ASA C) ∆ABC≅∆DEF by SAS D) ∆ABC≅∆DEF by CPCTC
∆JKL≅∆PQR by SAS
Which of the following statements is true based on the figures below? A) ∆JKL≅∆PQR by SSS B) ∆JKL≅∆PQR by SAS C) ∆JKL≅∆PQR by ASA D) ∆JKL≅∆PQR by CPCTC
∠1 and ∠4
Which pair of angles are vertical angles? A) ∠1 and ∠2 B) ∠1 and ∠3 C) ∠1 and ∠4 D) ∠2 and ∠4
∆ABC≅∆TUV
Which pair of triangles are congruent by SSS? A)∆ PQR≅∆DEF B) ∆XYZ≅ ∆JKL C) ∆ABC≅∆TUV D) ∆ABC≅∆DEF
Points A, B, E, and F are coplanar.
Which statement about the figure below is false? A) Points A, C, and E are coplanar. B) Two planes are pictured. C) Points A, B, E, and F are coplanar. D) Points A and D are not coplanar.
Points A, H, B, and F are coplanar.
Which statement about the figure below is false? A) Points E, B, C, and F are coplanar. B) Points E and F are collinear. C) Points A and D are collinear. D) Points A, H, B, and F are coplanar.
Line AB lies on both planes.
Which statement about the figure below is true? A) Line AB lies on plane P but doesn't lie on plane Q. B) Line AB lies on plane Q but doesn't lie on plane P. C) Line AB lies on both planes. D) Point A and plane P are collinear.
Line AB lies on plane BCD.
Which statement about the figure is false? A) Points D, B, and C are coplanar. B) Line AB lies on plane BCD. C) Lines AE and BC intersect at point B. D) Points A, B, and E are collinear.
X >Y
Which statement about the figure is true? A) X >Y B) X<Y C) X=Y D) cannot be determined
If a polygon does not have four sides, then it is not called a quadrilateral.
Which statement is the inverse of the following? "If a polygon has four sides, then it is called a quadrilateral." A) If a quadrilateral has four sides, then it is called a polygon. B) If a polygon is called a quadrilateral, then it has four sides. C) If a polygon is not called a quadrilateral, then it does not have four sides. D) If a polygon does not have four sides, then it is not called a quadrilateral.
p↔q
Which symbol is associated with a biconditional statement? A) ~p→q B) p↔q C) q→~p D) ~q→p
A, E, and D
Which three points are collinear in the figure below? A) A, E, and F B) D, F, and C C) A, E, and D D) B, G, and C
A, E, and C
Which three points are collinear in the figure below? A) A, B, and C B) A, B, and D C) D, E, and C D) A, E, and C
