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WorksheetsGrade 8 Geometry
Total questions: 72
Worksheet time: 36mins
Which of the following is not possible?
A plane and a line have no point in common.
A plane and a line have exactly one point in common.
A plane and a line have exactly two points in con1mon.
A plane and a line have more than two points in common.
Pick the correct statement.
A plane has exactly three points.
Line AB and plane (ABC) have only points A and B in common.
Two planes intersect at exactly one POINT.
If X ∈ AB and AB ⊂ C plane (P) then X ∈ plane (P).
Pick the correct statement.
Any two points are coplanar.
Any three points are non-coplanar.
Any three points are non-collinear.
Two planes intersect at exactly one point.
Pick the correct statement.
plane (ABE) ⋂ plane (BCE) = {E}
AC ⋂ BE = ⊘
O ∉ plane (ABC)
plane (ABC) ⋂ DE = ⊘
What is the intersection of plane EDB and plane EAC?
DB
AC
Point E
EO
Name three distinct planes that contain O
(ABG), (ADG), and (EDE)
(OBG), (ODG), and (ODA)
(ABC), (AEG), and (EDE)
(EBG), (BAB), and (BAD)
lf M is between A and B, then
AB ⋃ MB = MB
AB ⋂ MB = MB
AB ⋂ MB = {B}
AB ⋂ MB = MB
If M is between A and B such that AM = 2x, AB = 3x-1, and MB = 11, then x =
-4
14
8
12
Which of the following is not true?
AB ≅ BA
If A, B, and C are collinear, then AB = AC
As sets of points AB = BA
AB is the opposite of BA
If m separates plane Pinto two half planes, R1 and R2, then
R1 ⋂ R2 = ⊘
R1 ⋃ R2 = P
R1 ⋂ R2 = m
m ⊂ R1
If AB ≅ BD then AB = BD. then statement is true by:
Definition of midpoint
Definition of congruent segments
Definition of "betweeness"
The symmetric property
AD = 20, BC = 7, and B is midpoint of AC find AB
7
6
14
5
Which of the following can be deduced from the fact M between A and B
AM ≅ MB
MA and MB are opposite rays
AM < MB
AB + BM = AM
Refer to the diagram below to answer the question, Which of the following is another name for ∠1?
∠AOC
∠O
∠COB
∠AOB
Which of the following is closest to measure of angle AOC?
110°
80°
30°
170°
m∠AOC = (3x+2)°, m∠AOB = (x+2)°, and m∠BOC = 80°, Find x
20
25
30
40
In each case, the number on the outer edge of the semi-circle indicates the measure of the angle formed by OX and ray that contains the dashed line. Find m∠AOY
90°
100°
80°
180°
Refer to the diagram below to answer the question, Pick the angle vertically opposite to ∠BOD?
∠AOC
∠AOB
∠BOF
∠AOE
Refer to the diagram below to answer the question, Pick the angle adjacent to ∠BOD?
∠AOC
∠AOB
∠BOF
∠AOE
Two angles are supplementary whenever they
are adjacent
are vertically opposite
from a linear pair
are both obtuse
The supplement of a right angle is:
Acute
Right
Obtuse
Straight
If the measure of ∠1 is x° (0 ˂ x ˂ 90) then the measure of the complement is:
90° + x
180° + x
180° - x
90° - x
Refer to the diagram below to answer the question. m∠BJC = m∠AJC - m∠AJB is a direct consequence of
the ruler postulate
the protractor postulate
angle addition postulate
definition of a right angle
Which of the following is true about a scalene triangle?
Two of its side may be equal.
Two of its angles must be congruent.
Two of its angles may be congruent.
One of its angle may be obtuse.
Pick the correct statement.
In the obtuse triangle, all angles are obtuse.
In the acute triangle, all angles are acute.
In a right triangle, all angles are right.
In a isosceles triangle, all sides are equal.
If R is the interior of ∆ABC and P is a point on AR, the point P
must be in the interior of ∆ABC.
must be in the exterior of ∆ABC.
must be on ∆ABC.
could be in any one of the sets in the previous three choices.
Refer to the diagram below to answer the question. Given AB ≅ BC and ∠1 ≅ ∠2. ∆ABD ≅ ∆CBD by
ASA theorem.
SAS postulate.
SSS theorem.
The two triangles are not necessarily congruent.
∆ABC ≅ ∆EFG and ∆EGF ≅ ∆MNP (notice the change in the letters in EFG). What can be said about ∆ABC and ∆MNP?
They are not congruent.
∆ABC ≅ ∆MNP
∆ABC ≅ ∆MPN
∆ABC ≅ ∆PMN
What type of triangle is ∆ABC if it is given that ∆ABC ≅ ∆BCA?
∆ABC is isosceles but not equilateral.
∆ABC is not isosceles.
∆ABC is equilateral.
∆ABC is right.
If ∆RTS is isosceles with vertex R and base angles T and S, then
∆RTS ≅ ∆TRS
∆RTS ≅ ∆RST
∆RTS ≅ ∆TSR
∆RTS ≅ ∆STR
Which of the following is necessarily true about ∆ABC if it is given that ∆ABC ≅ ∆MNP and that ∆MNP is a right isosceles triangle?
I) ∆ABC is right, II) ∆ABC is isosceles
Only I is true.
Only II is true.
Both I and II must be true.
Neither l nor II are necessarily true.
Refer to the diagram below to answer the question. Given ∠ADB ≅ BDC and ∠1 ≅ ∠2. ∆ABD ≅ ∆CBD by
ASA theorem.
SAS postulate.
SSS theorem.
The two triangles are not necessarily congruent.
Which of the following is not possible about two congruent triangles?
One is acute while the other is scalene.
One is isosceles while the other is equilateral.
One is acute while the other is obtuse.
One is right while the other is isosceles.
Which of the following can be deduced from the figure?
M is the midpoint of CB.
∆BC is equilateral.
AB = AC
M is between B and C.
Given that ∠a and ∠b are complementary, ∠a and ∠x are supplementary, and ∠c and ∠x are supplementary, Which of the following is true?
∠b ≅ ∠c
∠a ≅ ∠b
∠b and ∠c are complementary
∠a and ∠c are supplementary
Which of the following cannot be deduced from the figure?
SH ⊥ RT
∠L ≅ ∠T
SP // RT
H is between R and T.
Refer to the diagram below to answer the question. Which triangle is ∠EBC exterior to?
∆EBD
∆EBA
∆ABC
∆ABD
Refer to the diagram below to answer the question. Which of the following is true?
m∠BEC > m∠A
m∠BEC ˃ m∠EBD
m∠C > m∠A
m∠BEC < m∠EBD
Refer to the diagram below to answer the question. Name the two remote interior angles to ∠BEC.
∠ECB and ∠EBC
∠BED and ∠EBD
∠BAD and ∠ABD
∠EDB and ∠EBD
Which of the following statement is equivalent to "If n is a natural number ending with 0 then n is divisible by 5"?
If n is a natural number not ending with 0 then n is not divisible by 5.
If n is divisible by 5 then n is a natural number ending with O.
If n is not divisible by 5 then n is a natural number not ending with 0.
Only natural numbers ending with O are divisible by 5.
Which of the following has the same truth value as ~ A => B?
A ∨ B
~ A ∨ B
A ∧ B
~ A ∧ B
Refer to the diagram below to answer the question. Which of the following cannot be deduced from the figure?
∠AMH and ∠CMH form a linear pair.
∠AMH and ∠CMH are supplementary.
M is between A and C.
HM ⊥ BC
If ∠A and ∠B are supplementary and ∠A is not right then either ∠A or ∠B is acute. To prove the above claim is true using the indirect method one assumes that:
only ∠A is not acute.
only ∠B is not acute.
both ∠A and ∠B are not acute.
∠A is a right angle.
Refer to the diagram below to answer the question. Pick the correct statement.
m∠A < 85°
m∠B < 85°
m∠A = m∠B
m∠B < 95°
Refer to the diagram below to answer the question. Find x.
90°
45°
60°
40°
Refer to the diagram below to answer the question. Find y.
80°
90°
50°
100°
Refer to the diagram below to answer the question. Find z.
50°
60°
70°
80°
The measures of the angles of a pentagon are x, 2x, 3x, 4x and 140°. Find x.
40°
50°
60°
70°
The measures of the angles of a quadrilateral are x, 2x, 3x, and 4x. Find the largest measure of all of the exterior angles of the quadrilateral.
108°
160°
144°
36°
The measure of an exterior angle of a regular octagon is equal to:
45°
135°
30°
150°
Which of the following is a regular polygon?
I- A rhombus
II- A rectangle
III- A square
I only
II only
III only
I, II, and Ill
Refer to the diagram below to answer the question. The two triangles are congruent as a direct consequence of
HL theorem
SAS postulate
HA corollary
None of the above
Refer to the diagram below to answer the question. The two triangles are congruent as a direct consequence of
HL theorem
SAS postulate
HA corollary
AAS postulate
Refer to the diagram below to answer the question. If a, b, and care the length of the sides as indicated by the diagram then
a < b < c
b < a < c
b < c < a
a < c < b
Which of the following is enough to guarantee the existence of a triangle with sides of length x, y, and z?
I- 0o < x < y < z
II- x + y > z
III- x - y = z
I only
II only
I and II
II and III
Refer to the diagram below to answer the question. Which of the following is a median in ∆ABC?
Only BE
Only AD
BE and AD
BE and AB
Refer to the diagram below to answer the question. Which of the following is altitude in ∆ABC?
Only AB
Only AD
AB and AC
None of the above
Refer to the diagram below to answer the question. Which of the following is an angle bisector in ∆ABC?
Only BE
Only BD
BE and AD
None of the above
Refer to the diagram below to answer the question. Find x
36°
18°
54°
27°
Refer to the diagram below to answer the question. MA = 10, MB = 7, MC= 7, MD = 6, M belongs to the perpendicular bisector of
AC
BC
AD
BD
Refer to the diagram below to answer the question. Line k is a transversal with respect to lines a and b. Which engle when combined with ∠2 forms a pair of alternate interior angles?
∠1
∠3
∠4
∠5
Refer to the diagram below to answer the question. Line k is a transversal with respect to lines a and b. Which engle when combined with ∠2 forms a pair of corresponding angles?
∠1
∠3
∠4
∠5
Refer to the diagram below to answer the question. Line k is a transversal with respect to lines a and b. Which engle when combined with ∠2 forms a pair of interior angles on the same side of k?
∠1
∠3
∠4
∠5
Refer to the diagram below to answer the question. Line k is a transversal with respect to lines a and b. Which engle when combined with ∠2 forms a linear pair?
∠1
∠3
∠4
∠5
Refer to the diagram below to answer the question. Find x if a // b.
30°
35°
40°
45°
Refer to the diagram below to answer the question. Find x if l // k.
30°
35°
40°
45°
Refer to the diagram below to answer the question. Pick the most appropriate answer. If m∠1 = m∠2 then
m // n as alternate interior angles are congruent.
m // n as corresponding interior angles are congruent.
t // s as corresponding interior angles are congruent.
t // s as alternate interior angles are congruent.
Refer to the diagram below to answer the question. What relation exists between x, y, and z?
x+ y = 180°
x + y + z = 360°
x = y
x + z = 180°
Refer to the diagram below to answer the question. Find x
30°
35°
40°
45°
Refer to the diagram below to answer the question. Given l // AB, Pick the correct statement. m∠B is equal to
m∠1
m∠2
90° - m∠1
180° - m∠2
Which statement is false?
If a line is perpendicular to one of two parallel lines it must he perpendicular to the other.
If a line is parallel to one of two parallel lines it must be parallel to the other.
If a line cuts one of two parallel lines it must cut the other.
In a plane through a given point many lines can be drawn parallel to a given line.
Pick the correct statement. If two parallel lines are cut by a transversal then
Interior angles on the same side of the transversal are congruent.
Alternate interior angles are supplementary.
Corresponding angles are congruent.
Corresponding angles ace supplementary.
