If ΔRST symbol ΔNPQ, which of the following is true?
(1 point)
Responses
∠R symbol ∠P
∠ R Image with alt text: symbol ∠ P
∠R symbol ∠Q
∠ R Image with alt text: symbol ∠ Q
∠T symbol ∠P
∠ T Image with alt text: symbol ∠ P
∠T symbol ∠Q
Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
Responses
22
22
11
11
10
10
25
Use the image to answer the question.
The figure shows triangle J K N and triangle L K M formed by intersecting segments J M and N L at point K. Segment J K is marked with 2 hash marks. Segment K L is marked with 2 hash marks. Segment N K is marked with 1 hash mark. Segment K M is marked with 1 hash mark.
Which of the following statements is true about the triangles?
(1 point)
Responses
Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper Lby SSS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper L by SSS
Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper Jby AAS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper J by AAS
Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper Mby ASA
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper M by ASA
Triangle Upper J Upper K Upper N congruent to triangle Upper L Upper K Upper Mby SAS
triangle upper T upper I upper C is an Isosceles triangle with a vertex angle I. If the measure of angle upper I equals 90 degrees, then find the measure of angle upper T.
(1 point)
Responses
15°
15°
45°
45°
90°
90°
30°
True or False
All right triangles are isosceles.
(1 point)
Responses
true
true
false
Justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: ΔABC is congruent to ΔCDA
The figure shows parallelogram A B C D with diagonal A C.
ABDC is a parallelogram.
AB is congruent to DC and BC is congruent to DA
AC is congruent to CA
ΔABC is congruent to ΔCDA
Given
Opposite sides of a parallelogram are congruent.
_____________________?
_____________________?
(1 point)
Responses
Transitive Property of congruent; SAS
Transitive Property of Image with alt text: congruent ; SAS
Reflexive Property of congruent; SAS
Reflexive Property of Image with alt text: congruent ; SAS
Transitive Property of congruent; SSS
Transitive Property of Image with alt text: congruent ; SSS
Reflexive Property of congruent; SSS
Reflexive Property of Image with alt text: congruent ; SSS
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Question
Which triangles are congruent by AAS?
Three triangles are shown with markings on sides and angles.Triangle V T U has one tick mark on side T U, one angle mark on angle T, and two angle marks on angle V.
Triangle H F G has two tick marks on side H F, one angle mark on angle F, and two angle marks on angle H.
Triangle C A B has one tick mark on side A B, two tick marks on side C A, one angle mark on angle A, and two angle marks on angle C.
(1 point)
Responses
Triangle V T U and Triangle C A B
Image with alt text: Triangle V T U and Image with alt text: Triangle C A B
Triangle V T U and Triangle H F G
Image with alt text: Triangle V T U and Image with alt text: Triangle H F G
Triangle H F G and Triangle C A B
Image with alt text: Triangle H F G and Image with alt text: Triangle C A B
none of the above
none of the above
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Question
Use the image to answer the question.
The figure shows an isosceles triangle with an altitude drawn from the top vertex to the lower side. The left and right sides are each marked with 1 tick mark. The altitude is shown to meet the lower side at a right angle.
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?
(1 point)
Responses
SAS
SAS
HL
HL
ASA
ASA
none
none
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Question
Find the value of x.
The figure shows a triangle with the left and right sides each marked with 1 tick mark. The top interior angle is 30 degrees. The lower left interior angle is x degrees.
(1 point)
Responses
75
75
70
70
60
60
80
80
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Question
Find the value of x.
An isosceles triangle is shown and the horizontal base at the bottom of the triangle extends out to the left of the triangle. The angle at the bottom right corner of the triangle and the exterior angle formed by the left side of the triangle and the horizontal line that extends at the bottom left of the image are labeled.An isosceles triangle is shown. The horizontal line at the bottom of the triangle extends out to the left of the triangle. The bottom right corner of the triangle is labeled left-parenthesis 3 x plus 8 right-parenthesis degrees. An exterior angle at the bottom left of the image is formed by the left side of the triangle and the horizontal base of the triangle that extends out past the triangle. This angle is labeled left-parenthesis 5 x plus 12 right-parenthesis degrees.
(1 point)
Responses
10
10
15
15
20
20
25
25
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Question
What are the missing reasons in the two-column proof?
Given: modifying above with right arrow upper M upper O bisects angle upper P upper M upper N and modifying above with right arrow upper O upper M bisects angle upper P upper O upper N
Prove: triangle upper P upper M upper O congruent to triangle upper N upper M upper O
A two column proof and a diagram are shown.A two column proof is shown. In the statements column there are 6 statements. 1 says modifying above with right arrow upper M upper O bisects angle upper P upper M upper N. 2 says angle upper P upper M upper O congruent to angle upper N upper M upper O. 3 says modifying above with bar upper M upper O congruent to modifying above with bar upper M upper O. 4 says modifying above with right arrow upper O upper M bisects angle upper P upper O upper N. 5 says angle upper P upper O upper M congruent to angle upper N upper O upper M. 6 says triangle upper P upper M upper O congruent to triangle upper N upper M upper O. In the reasons columns there are the numbers 1 through 6 but each reason is blank with a question mark. The diagram is also shown. Line upper M upper O is horizontal across the middle of the diagram. Point upper N is at the top of the diagram and two lines extend from it down to line upper M upper O forming a triangle. Another point upper P is at the bottom of the diagram and two lines extend from it up to line upper M upper O forming another triangle. The two triangles appear congruent and share two vertices on line upper M upper O.
(6 points)
SQuestion
Is trianglePQS congruent to triangleRQS by HL? If so, name the legs that allow the use of HL.
Triangle P S R is shown with altitude S Q from vertex S to point Q on side P R. Side P S is marked congruent to Side S R.
(2 points)
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Question
Short Answer
Your teacher will grade your responses for questions 13–15, to ensure that you receive proper credit for your answers.
Write a paragraph proof.
Given: modifying above B C with bar congruent to modifying above E C with bar and Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
Prove: modifying above upper B upper A with barcongruent to Modifying above Upper E Upper D with bar
Segment B A is shown on the left. Segment D E is shown on the right. Segment B E intersects Segment A D at point C.
(5 points)
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Question
Short Answer
Using the words from the word list, name all the parts of the isosceles triangle in the diagram below. Some words may be used more than once.
A diagram of a triangle, a corresponding word list, and answer spaces are shown.
· Triangle upper A upper C upper E is shown with segment upper A upper C and segment upper E upper C each labeled with the same tick mark.
· Upper B is located on upper A upper C.
· Upper D is located on upper E upper C.
· Upper F is located on upper A upper E.
· The word list contains vertex angle, base angle, leg, and base.
The answer spaces are:
· upper A large dash
· upper B large dash
· upper C large dash
· upper D large dash
· upper E large dash
· upper F large dash
(4 points)
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Question
Short Answer
What does CPCTC represent and when would you use it?
(2 points)
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Question
Essay
Your teacher will grade your response to ensure that you receive proper credit for your answer.
It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
The image of a baseball diamond is shown. The diamond itself is a square rotated so that a vertex is on the bottom. The bottom vertex is labeled 'Home,' the right vertex is labeled 'First,' the top vertex is labeled 'Second,' and the left vertex is labeled 'Third.' There is a diagonal drawn connecting 'Second' and 'Home.'
(6 points)
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I'm sorry, but I'm not able to answer your question.
(1 point)
Responses
∠R symbol ∠P
∠ R Image with alt text: symbol ∠ P
∠R symbol ∠Q
∠ R Image with alt text: symbol ∠ Q
∠T symbol ∠P
∠ T Image with alt text: symbol ∠ P
∠T symbol ∠Q
Given triangleABC congruent to trianglePQR, mangleB = 3v + 4, and mangleQ = 8v – 6, find mangleB and mangleQ.
(1 point)
Responses
22
22
11
11
10
10
25
Use the image to answer the question.
The figure shows triangle J K N and triangle L K M formed by intersecting segments J M and N L at point K. Segment J K is marked with 2 hash marks. Segment K L is marked with 2 hash marks. Segment N K is marked with 1 hash mark. Segment K M is marked with 1 hash mark.
Which of the following statements is true about the triangles?
(1 point)
Responses
Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper Lby SSS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper L by SSS
Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper Jby AAS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper J by AAS
Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper Mby ASA
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper M by ASA
Triangle Upper J Upper K Upper N congruent to triangle Upper L Upper K Upper Mby SAS
triangle upper T upper I upper C is an Isosceles triangle with a vertex angle I. If the measure of angle upper I equals 90 degrees, then find the measure of angle upper T.
(1 point)
Responses
15°
15°
45°
45°
90°
90°
30°
True or False
All right triangles are isosceles.
(1 point)
Responses
true
true
false
Justify the last two steps of the proof.
Given: ABCD is a parallelogram.
Prove: ΔABC is congruent to ΔCDA
The figure shows parallelogram A B C D with diagonal A C.
ABDC is a parallelogram.
AB is congruent to DC and BC is congruent to DA
AC is congruent to CA
ΔABC is congruent to ΔCDA
Given
Opposite sides of a parallelogram are congruent.
_____________________?
_____________________?
(1 point)
Responses
Transitive Property of congruent; SAS
Transitive Property of Image with alt text: congruent ; SAS
Reflexive Property of congruent; SAS
Reflexive Property of Image with alt text: congruent ; SAS
Transitive Property of congruent; SSS
Transitive Property of Image with alt text: congruent ; SSS
Reflexive Property of congruent; SSS
Reflexive Property of Image with alt text: congruent ; SSS
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Question
Which triangles are congruent by AAS?
Three triangles are shown with markings on sides and angles.Triangle V T U has one tick mark on side T U, one angle mark on angle T, and two angle marks on angle V.
Triangle H F G has two tick marks on side H F, one angle mark on angle F, and two angle marks on angle H.
Triangle C A B has one tick mark on side A B, two tick marks on side C A, one angle mark on angle A, and two angle marks on angle C.
(1 point)
Responses
Triangle V T U and Triangle C A B
Image with alt text: Triangle V T U and Image with alt text: Triangle C A B
Triangle V T U and Triangle H F G
Image with alt text: Triangle V T U and Image with alt text: Triangle H F G
Triangle H F G and Triangle C A B
Image with alt text: Triangle H F G and Image with alt text: Triangle C A B
none of the above
none of the above
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Question
Use the image to answer the question.
The figure shows an isosceles triangle with an altitude drawn from the top vertex to the lower side. The left and right sides are each marked with 1 tick mark. The altitude is shown to meet the lower side at a right angle.
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?
(1 point)
Responses
SAS
SAS
HL
HL
ASA
ASA
none
none
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Question
Find the value of x.
The figure shows a triangle with the left and right sides each marked with 1 tick mark. The top interior angle is 30 degrees. The lower left interior angle is x degrees.
(1 point)
Responses
75
75
70
70
60
60
80
80
Skip to navigation
Question
Find the value of x.
An isosceles triangle is shown and the horizontal base at the bottom of the triangle extends out to the left of the triangle. The angle at the bottom right corner of the triangle and the exterior angle formed by the left side of the triangle and the horizontal line that extends at the bottom left of the image are labeled.An isosceles triangle is shown. The horizontal line at the bottom of the triangle extends out to the left of the triangle. The bottom right corner of the triangle is labeled left-parenthesis 3 x plus 8 right-parenthesis degrees. An exterior angle at the bottom left of the image is formed by the left side of the triangle and the horizontal base of the triangle that extends out past the triangle. This angle is labeled left-parenthesis 5 x plus 12 right-parenthesis degrees.
(1 point)
Responses
10
10
15
15
20
20
25
25
I'm sorry, but I cannot answer these questions as they require visual information that I cannot see.
To determine which of the following statements is true about the triangles, we need to compare the corresponding angles of the two triangles.
In the given question, ΔRST is stated to be symbol ΔNPQ. This symbol signifies that the two triangles are congruent, meaning their corresponding angles and sides are equal.
To find the true statement, we need to determine which angles of ΔRST correspond to which angles of ΔNPQ.
We can use the following corresponding angle symbols to represent the angles of the two triangles:
∠R symbol ∠P
∠T symbol ∠Q
Based on these corresponding angle symbols, we can conclude that the statement "∠R symbol ∠P" is true. This means that angle R in ΔRST is congruent to angle P in ΔNPQ.