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WorksheetsGeometry Concepts and Theorems MYA
Total questions: 150
Worksheet time: 5hrs 22mins
Which pair of angles are alternate interior angles when two parallel lines are cut by a transversal?
Angles on the same side of the transversal and inside the lines
Angles on opposite sides of the transversal and inside the lines
Angles on the same side of the transversal and outside the lines
Angles on opposite sides of the transversal and outside the lines
If ∠ABC and ∠DEF are alternate interior angles and the lines are parallel, what can you conclude?
∠ABC=∠DEF
∠ABC+∠DEF=180∘
∠ABC=2∠DEF
∠ABC and ∠DEF are supplementary
According to the Angle Addition Postulate, if point D is in the interior of ∠ABC , then:
∠ABD+∠DBC=∠ABC
∠ABD=∠DBC
∠ABD−∠DBC=∠ABC
∠ABD+∠DBC=180∘
If ∠1 and ∠2 are congruent supplements, what is the measure of each angle?
45∘
60∘
90∘
120∘
Which statement best describes an angle bisector?
A ray that divides an angle into two congruent angles
A line that divides a segment into two equal parts
A line that is perpendicular to a segment at its midpoint
A segment joining two non-adjacent vertices of a polygon
Given the conditional statement: "If a figure is a square, then it has four right angles." What is the hypothesis?
The figure has four right angles
The figure is a square
The figure is a rectangle
The figure has equal sides
The centroid of a triangle divides each median into what ratio?
1:1
1:2
2:1
3:1
If ∠ABC is bisected by ray BD , and m∠ABD=35∘ , what is m∠DBC ?
35∘
70∘
17.5∘
45∘
If two angles are supplements and one measures x∘ , what is the measure of the other angle?
90∘
180∘−x
x∘
180∘+x
Which of the following is a counterexample to the statement: "All quadrilaterals are rectangles"?
Square
Parallelogram
Rectangle
Rhombus
If G is the centroid of △ABC with vertices A(0,0) , B(6,0) , and C(0,6) , what are the coordinates of G ?
(2,2)
(3,3)
(2,3)
(1,1)
Which of the following is the converse of the statement: "If two lines are parallel, then alternate interior angles are congruent"?
If alternate interior angles are congruent, then two lines are parallel
If two lines are not parallel, then alternate interior angles are not congruent
If two lines are parallel, then alternate interior angles are not congruent
If alternate interior angles are not congruent, then two lines are not parallel
If ∠1 and ∠2 are congruent and supplementary, what is the value of m∠1 ?
60∘
90∘
120∘
180∘
Which of the following is true about the centroid of a triangle?
It is the intersection of the angle bisectors
It is the intersection of the medians
It is the intersection of the altitudes
It is the intersection of the perpendicular bisectors
If m∠ABD=40∘ and m∠DBC=30∘ , what is m∠ABC by the Angle Addition Postulate?
70∘
60∘
110∘
10∘
Which of the following is a conditional statement?
All triangles have three sides.
If a figure is a triangle, then it has three sides.
Triangles are polygons.
A triangle has three angles.
If a ray bisects an angle of 80∘ , what is the measure of each resulting angle?
80∘
40∘
20∘
60∘
Which of the following is NOT a property of an angle bisector?
It divides an angle into two congruent angles
It always passes through the centroid
It starts at the vertex of the angle
It creates two adjacent angles
If two parallel lines are cut by a transversal, which angles are always congruent?
Alternate interior angles
Consecutive interior angles
Adjacent angles
Linear pair angles
If m∠1=3x+10 and m∠2=5x−6 are congruent supplements, what is the value of x ?
12
22
24
48
Which of the following best describes the conclusion of the conditional statement: "If a polygon is a rectangle, then it has four right angles"?
The polygon is a rectangle
The polygon has four right angles
The polygon is a square
The polygon has equal sides
If the centroid of a triangle is at (4,2) and one vertex is at (1,2) , another at (7,2) , what is the x -coordinate of the third vertex?
4
3
5
2
Which of the following is an example of a conditional statement?
All squares are rectangles.
If a number is even, then it is divisible by 2.
Triangles have three sides.
A rectangle has four sides.
If m∠ABD=2x+10 and m∠DBC=x+20 , and m∠ABC=80∘ , what is the value of x ?
10
20
30
40
Which of the following is true about alternate interior angles?
They are always supplementary
They are congruent if the lines are parallel
They are always adjacent
They are always vertical angles
If the centroid of a triangle is at (2,3) and two vertices are at (1,2) and (4,5) , what are the coordinates of the third vertex?
(1,2)
(1,2)
(1,2)
(1,2)
If two angles are congruent supplements, what is the sum of their measures?
90∘
180∘
360∘
270∘
Which of the following is the correct definition of an angle bisector?
A line that divides a segment into two equal parts
A ray that divides an angle into two congruent angles
A line that is perpendicular to a segment at its midpoint
A segment joining two non-adjacent vertices of a polygon
If m∠ABD=25∘ and m∠DBC=65∘ , what is m∠ABC ?
40∘
90∘
100∘
120∘
Which of the following is a property of the centroid of a triangle?
It is always outside the triangle
It divides each median into a 2:1 ratio
It is the intersection of the angle bisectors
It is the intersection of the altitudes
∠1 and ∠3 are
(a) angles
vertical
linear
adjacent
angry
Match the following angle pair to its relationship.
3 & 6
Complementary
2 & 6
Adjacent
5 & 6
Vertical
2
Right angle
1 & 4
No relationship
The angle relationship shown is - (a)
supplementary angles
complementary angles
vertical angles
adjacent angles
Match the following
∠1 and ∠4
Vertical Angles
∠1 and ∠7
Consecutive Exterior Angles
∠3 and ∠5
Consecutive Interior Angles
∠5 and ∠4
Alternate Interior Angles
Use the diagram for the matching exercise.
1 and 2
Supplementary
5 and 7
Vertical
2 and 6
Corresponding
3 and 5
Alternate Interior
1 and 7
Alternate Exterior
If the measure of ∠ADC is
50 degrees, then what is the measure of ∠BDC?
17.3 degrees
32.7 degrees
∠ADC = 50 degrees
Based on the graph, match each pair of angles with the relationship of their measures.
1 & 7
Congruent
4 & 5
Supplementary
2 & 3
Supplementary
2 & 6
Congruent
Match the following angle pair to its relationship.
a & z
Corresponding
r & g
Alternate Interior
e & d
Alternate Exterior
a & d
Linear Pair
d & c
Consecutive Exterior
Find the measure of angle A,
Find the angle indicated.
Use the map to match angle examples of each relationship.
∠1 & ∠6
vertical angles
∠1 & ∠3
corresponding angles
∠1 & ∠17
supplementary angles
∠1 & ∠2
linear pair
∠1 & ∠18
congruent angles
∠b and∠g are (a) angles
Alternate Exterior
Alternate Interior
Consecutive Exterior
Bestie Angles
Vertical Angles
Match the following: Given the figure on the left, match the given paired angles to its correct name.
∠ 12 and ∠6
Alternate Exterior
∠19 and ∠15
Alternate Interior
∠17 and ∠22
Vertical Angles
∠5 and ∠16
Corresponding Angles
∠8 and ∠13
Same-Side Interior (Consecutive Interior)
Same-Side Interior angles are (a) the lines, l and m, and on the (b) of the transversal, and they are only (c) if the lines are parallel .
Angles 3 and 5 are a pair of Alternate Interior Angle, and another pair is angles (d) and (e) .
inside
same side
supplementary
4
6
1
7
outside
The angle relationship shown is - (a)
supplementary angles
complementary angles
vertical angles
adjacent angles
Find the measure of angle A,
Alternative Interior angles are (a) the lines, l and m, and on the (b) of the transversal, and they are only (c) if the lines are parallel .
Angles 3 and 6 are a pair of Alternate Interior Angle, and another pair is angles (d) and (e) .
inside
opposite side
congruent
4
5
1
7
outside
same side
supplementary
Match the following angles
∠1 and ∠7 are
same side exterior angles
∠2 and ∠5 are
corresponding
angles
∠1 and ∠6 are
alternate exterior angles
∠5 and ∠7 are
vertical angles
What is the Geometry Set up and the Equation for this problem?
(x+8)
m∠ACB
m∠ACD
(9x-18)
What is the relationship of the Angles
Alternate Interior
Alternate Exterior
Corresponding
vertical
Which pair of angles are alternate exterior angles?
Angle 7 and Angle 4
Angle 2 and Angle 6
Angle 8 and Angle 1
Angle 2 and Angle 8
What are supplementary angles?
Angles that add up to 180°
Angles that add up to 90°
Angles that are equal to each other
Angles that are opposite of each other when lines intersect
Name the angle relationship.
Consecutive Interior
Alternate Interior
Corresponding
Vertical Angles
Name the alternate interior angle to angle 3.
4
5
6
8
State the angle relationship and find the measure of angle 2
Alternate Exterior
127
Alternate Exterior
52
Alternate Interior
127
Alternate Interior
52
Find m ∠C.
∠C=116°
∠C=64°
∠C=180°
∠C=26°
Which of these angles is NOT congruent to angle 5?
Angle 6
Angle 8
Angle 1
Angle 4
A line that passes through parallel lines is called a ______________.
vertical lines
a passer through line
transversal
perpendicular line
Name the angle relationship.
Alternate Interior
Alternate Exterior
Corresponding
Vertical Angles
Name the angle relationship.
Same Side Interior
Alternate Interior
Corresponding
Vertical Angles
Name the angle relationship.
Same Side Interior
Corresponding
Alternate Interiors
Linear Pairs
What is necessary for the lines to be parallel?
Same Slope
Same intercept
Negative Flip of the slope
None of the above
What does lines being parallel mean?
The lines don't like each other.
The lines always intersect?
The lines never intersect.
Nobody knows. It's a mystery of math.
Two lines that have the same slope and intercept are:
Parallel
Perpendicular
The same line
None of the above
Identify the correct statement.
∠1 & ∠2
are vertical angles
∠2 & ∠4
are vertical angles
∠5 & ∠8
are vertical angles
∠1 & ∠5
are vertical angles
What is the value of x?
13
6.2
29.8
Name the angle relationship.
Consecutive Interior
Alternate Interior
Corresponding
Vertical Angles
A line that passes through parallel lines is called a ______________.
vertical lines
a passer through line
transversal
perpendicular line
Name the angle relationship.
Alternate Interior
Alternate Exterior
Corresponding
Vertical Angles
x = 118
x = 108
x = 28
x = 58
These angles are...
Complementary
Supplementary
Neither
75*
40*
55*
50*
Angles on the same side of a transversal, in corresponding positions, and are congruent are called _____.
Alternate Interior Angles
Alternate Exterior Angles
Adjacent Angles
Corresponding Angles
(a)
What does SSS stand for?
Small Small Small
Side Side Side
Small Side Small
Sam's Silly Side
What does SSS prove?
Nothing
Triangles similar
Triangles congruent
Triangle angle sum
Complete the congruence statement.
CRP
PCR
RPC
PRC
Name the postulate, if possible, that makes the triangles congruent.
SSS
SAS
ASA
Not Possible
State if the two triangles are congruent. If they are, state which theorem you would use.
Yes, SAS
Yes, SSS
Yes, HL
No
Name the postulate, if possible, that makes the triangles congruent.
SAS
ASA
SSS
Not Possible
Which would be the best classification for the triangle shown?
acute isosceles
equiangular scalene
equiangular isosceles
equiangular equilateral
Are the two triangles congruent?
Not enough information
Yes, by SSA
Yes by AAS
Yes By ASA
Are the triangles congruent, if yes, why?
SSS
SAS
ASA
Not Congruent
Figures that have the same _____ and size are congruent triangles.
corresponding
corners
angles
shape
Classify the triangle shown in the picture by its angles.
Obtuse
Right
Acute
Equilateral
Classify the triangle shown in the picture by its sides.
Equilateral
Scalene
Obtuse
Isosceles
Classify the triangle shown in the picture by its sides.
Isosceles
Obtuse
Equilateral
Scalene
Solve for x
x = 12
x = 4
x = 3.33
x = 10
Find the measure of Angle A.
40°
140°
80°
100°
Fill in the blank.
Given
Reflexive Property
Transitive Property
They're the same side!!!!!!
Which would be the best classification for the triangle shown?
acute isosceles
equiangular scalene
equiangular isosceles
equiangular equilateral
Which statement indicates that the triangles in each pair are congruent.
∆LMK ≅ ∆LMT
∆LMK ≅ ∆TMK
∆LTKM ≅ ∆LMT
∆TMK ≅ ∆TLK
Remember order matters. Which of the following is true?
∆FGH ≅ ∆VHW
∆HFG ≅ ∆HWV
∆HGF ≅ ∆VHW
∆FGH ≅ ∆VWH
Find the measure of the indicated angle.
34
46
62
36
Choose a correct equation to find x.
4x - 2 + 12x + 1 = 75
4x - 2 + 75 = 12x + 1
4x - 2 + 75 + 12x + 1 = 180
4x - 2 - 75
Solve for x.
6
8
15
13
What is the name of the triangle congruent to ΔRPE ?
ΔCFT
ΔFTC
ΔTFC
ΔFCT
Name the corresponding angle or side.
A
B
C
D
Including the Reflexive Property, state whether the triangles are congruent and why.
no, not enough information
yes, SAS
yes, ASA
yes, HL
State if the triangles are congruent and why.
AAS
SAS
ASA
SSS
State if the triangles are congruent and why.
Not congruent
AAS
SSS
ASA
State if the triangles are congruent and why.
AAS
ASA
Not congruent
SSS
Including the Reflexive Property, which theorem proves the triangles are congruent.
ASA
SSS
SAS
AAS
Using the Reflexive Property, which theorem proves that the triangles are congruent.
SAS
AAS
ASA
HL
What additional information is needed to prove the triangles congruent by SSS?
A
B
C
D
What is the relationship of the angles?
Alternate Interior
Alternate Exterior
Corresponding
Same-Side interior
What is the relationship of the angles?
Alternate Interior
Alternate Exterior
Same-Side Interior
Corresponding
What is the relationship of the angles?
Alternate Interior
Alternate Exterior
Same-Side Interior
Corresponding
What is the relationship of the angles?
Alternate Interior
Alternate Exterior
Corresponding
Same-Side Interior
What are supplementary angles?
Two angles that are on the same side of the transversal
Two angles that add up to equal 90°
Two angles that add up to 180°
Two angles that are corresponding
What are complementary angles?
Two angles that add up to 180°
Two angles that are alternate interior angles
Two angles that add up to 90°
Two angles that are same-side interior
Congruent by
SSS
SAS
ASA
AAS
Are these triangles congruent?
Yes, by AAS
Yes, by SAS
Yes, by SSS
No, this is the SSA one!!
∠E ≅ ∠ __
A
B
C
D
Which triangle congruence proves that the triangles are congruent?
SSS
SAS
ASA
Not Congruent
How are the triangles congruent?
HL
SSS
SAS
AAS
Which triangle congruence theorem can be used to prove the triangles are congruent?
ASA
AAS
SAS
AAA
What does congruent mean?
Same size, but different shape
Different size and different shape
Same size and the same angle measure
Different size, but same shape
According to the SSS Theorem. A triangle with side lengths 2, 4, and 6 would be congruent to which other triangle?
1,2,3
4,5,6
6,4,2
4,8,12
Which of the following is NOT an abbreviation used for Triangle Congruence Theorems?
ASA
SSA
SSS
SAS
Which theorem is used to prove that two triangles are congruent if two angles and the included side are equal?
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
Complete the congruence statement.
ΔCRP
ΔPCR
ΔRPC
ΔPRC
∆ABC ≅ ∆XYZ, which is true?
AB ≅ XY
AB ≅ YX
AB ≅ XZ
BC ≅ CB
Which pieces of information could you use to prove the triangles congruent? (Select multiple.)
m∠Q = m∠S
m∠P = m∠R
m∠POQ = m∠ROS
SO = QO
RO = PO
Name the postulate, if possible, that makes the triangles congruent.
SSS
SAS
ASA
AAS
Are these triangles congruent? If so, state the rule which you used to determine congruence.
AAA
AAS
ASA
Not necessarily congruent
Fill in the blank.
Given
Reflexive Property
Transitive Property
They're the same side!!!!!!
What congruence theorem proves triangle ABD is congruent to triangle CBE?
AAS
ASA
SAS
NEI
If the two triangles are congruent, answer with the criterion that proves them congruent.
SSS
Not Congruent
HL
SAS
AD is a perpendicular bisector. Solve for x
8
4
20
11
Solve for the value of x.
x = 10
x = 20
x = 3
x = 45
QR = 4
QR = 20
QR = 11
QR = 5
Angle ABC measures 34o. What is the measure of angle CBD?
17o
34o
68o
Name the perpendicular bisector.
Line CP
Segment AP
Segment AC
Line AB
D is the circumcenter, find EH
15
16
17
19
VT is a perpendicular bisector of triangle XYZ. What is the total length of XY?
30
20
10
15
if m∠VTY is 7x+20, what is the value of x?
13
10
20
15
FT is a perpendicular bisector of ΔPIG. Solve for x
6.58
18.75
3.12
Solve for x
18
32
20
Find m∠PRQ.
39°
90°
51°
15°
What is x?
15
23
2
92
What is the average number of students in each class if there are 250 students in 10 classes?
240
25
Mandy earns money by delivering groceries. She earned
$4 on Monday, $7 on Tuesday, $5 on Wednesday, $4 on
Thursday, and $5 on Friday. What is the average amount
of money Mandy earned per day?
25
5
21
Find the weighted average P when the coordinates of A, B & C are -2, 4 & 9 respectively,
given that Point B weighs twice as much as point A and point C weighs four times as much as point A.
Note: write your answer as a single number or P = your answer
(a)
Find the coordinate of A in Segment AB given that B is located at -5,
the weighted average P = 7, and point A weighs twice as much as point B.
Note: enter your answer as a single number
(a)
How do you find the average of a set of scores?
To find the average, sum all the scores and divide by the number of scores.
Multiply all the scores and then divide by the number of scores.
Add the highest and lowest scores and divide by two.
Count the number of scores and take the largest one.
How do you calculate a weighted average?
Multiply each score by its corresponding weight, sum all the products, and then divide by the total of the weights.
Add all the scores together and divide by the number of scores.
Take the highest score and multiply it by the total number of scores.
Calculate the average of the weights and then apply it to the scores.
What is the significance of weights in calculating averages?
Weights determine the influence of each score on the overall average; higher weights mean that score has a greater impact.
Weights are used to adjust the scores to fit a normal distribution.
Weights are irrelevant in calculating averages and can be ignored.
Weights only apply to statistical models and not to simple averages.
What is a weighted average?
A method of calculating the mean of a dataset without considering the importance of values.
An average that considers the relative importance of each value in a dataset, calculated by multiplying each value by its weight and dividing by the total weight.
A statistical measure that only takes the highest value in a dataset into account.
A technique used to find the median of a dataset by arranging values in order.
Why would you use a weighted average instead of a traditional average calculation?
Because you have a lot of numbers
Because the value you are trying to calculate is made up of categories which each have different weights.
