Question
Question 1
A)
Use the image to answer the question.
Four triangles are labeled upper A upper B upper C, upper E upper D upper C, upper A prime upper B prime upper C, and upper A double prime upper B double prime upper C, with the point upper C common to all three.
To prove △ABC≅△A′′B′′C′′, which of the following shows how the ASA criterion follows from the definition of congruence in terms of rigid motions?
(1 point)
Responses
Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across CA′¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C negative 90 degrees (clockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper C upper A prime with bar .
Rotate △ABC 360 degrees (counterclockwise), and then reflect △A′B′C′ across B′C¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C 360 degrees (counterclockwise), and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper B prime upper C with bar .
Rotate △ABC 90 degrees (counterclockwise) about vertex C, and then reflect △A′B′C′ across CA′¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C 90 degrees (counterclockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper C upper A prime with bar .
Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across B′C¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C negative 90 degrees (clockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper B prime upper C with bar .
Question 2
A)Which of the following pairs of triangles could be proven congruent by the ASA Congruence Theorem?(1 point)
Responses
Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Image with alt text: Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.
Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.
Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Image with alt text: Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Question 3
A)
Use the image to answer the question.
Three triangles are labeled upper A upper B upper C, upper M upper N upper P, and upper A prime upper B prime upper C prime.
Khalil is using rigid transformations to map △ABC to △MNP. What type of transformation does ray AA′ indicate?
(1 point)
Responses
Ray AA′ indicates a rotation.
Ray upper A upper A prime indicates a rotation.
Ray AA′ indicates a reflection.
Ray upper A upper A prime indicates a reflection.
Ray AA′ indicates a translation.
Ray upper A upper A prime indicates a translation.
Ray AA′ indicates a dilation.
Ray upper A upper A prime indicates a dilation.
Question 4
A)
Use the image to answer the question.
Parallelogram upper A upper D upper C upper B is graphed on a plane, with diagonal upper A upper C.
In parallelogram ABCD, diagonal AC¯¯¯¯¯¯¯¯ is drawn, and ∠BCA≅∠DAC and ∠BAC≅∠DCA . In order to prove △ABC≅△CDA by the ASA Congruence Theorem, what additional information must be stated and justified?
(1 point)
Responses
AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ by the Triangle Angle Sum Theorem.
Modifying above upper A upper B with bar congruent to Modifying above upper C upper D with bar by the Triangle Angle Sum Theorem.
AC¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.
Modifying above upper A upper C with bar congruent to Modifying above upper A upper C with bar by the Reflexive Property of Congruence.
DA¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.
Modifying above upper D upper A with bar congruent to Modifying above upper B upper C with bar by the Reflexive Property of Congruence.
∠B≅∠D by the Reflexive Property of Congruence.
angle upper B congruent to angle upper D by the Reflexive Property of Congruence.
Question 5
A)
Use the image to answer the question.
Two congruent triangles, upper A upper B upper C and upper B upper C upper D, are mirrored over side upper B upper C on a plane. B both angels B are congruent. Both angels C are congruent.
Based on the markings in the diagram, what additional information must be stated in order to prove △ABC≅△DBC by the ASA Congruence Theorem?
(1 point)
Responses
AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
∠A≅∠D
angle upper A congruent to angle upper D
BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
A)
Use the image to answer the question.
Four triangles are labeled upper A upper B upper C, upper E upper D upper C, upper A prime upper B prime upper C, and upper A double prime upper B double prime upper C, with the point upper C common to all three.
To prove △ABC≅△A′′B′′C′′, which of the following shows how the ASA criterion follows from the definition of congruence in terms of rigid motions?
(1 point)
Responses
Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across CA′¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C negative 90 degrees (clockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper C upper A prime with bar .
Rotate △ABC 360 degrees (counterclockwise), and then reflect △A′B′C′ across B′C¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C 360 degrees (counterclockwise), and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper B prime upper C with bar .
Rotate △ABC 90 degrees (counterclockwise) about vertex C, and then reflect △A′B′C′ across CA′¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C 90 degrees (counterclockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper C upper A prime with bar .
Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across B′C¯¯¯¯¯¯¯¯¯.
Rotate triangle upper A upper B upper C negative 90 degrees (clockwise) about vertex upper C , and then reflect triangle upper A prime upper B prime upper C prime across Modifying above upper B prime upper C with bar .
Question 2
A)Which of the following pairs of triangles could be proven congruent by the ASA Congruence Theorem?(1 point)
Responses
Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Image with alt text: Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.
Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.
Image with alt text: Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 columns by 5 row grid.
Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Image with alt text: Two congruent triangles, upper X upper Y upper Z and upper A upper B upper C are shown within an 11 column by 5 row grid.
Question 3
A)
Use the image to answer the question.
Three triangles are labeled upper A upper B upper C, upper M upper N upper P, and upper A prime upper B prime upper C prime.
Khalil is using rigid transformations to map △ABC to △MNP. What type of transformation does ray AA′ indicate?
(1 point)
Responses
Ray AA′ indicates a rotation.
Ray upper A upper A prime indicates a rotation.
Ray AA′ indicates a reflection.
Ray upper A upper A prime indicates a reflection.
Ray AA′ indicates a translation.
Ray upper A upper A prime indicates a translation.
Ray AA′ indicates a dilation.
Ray upper A upper A prime indicates a dilation.
Question 4
A)
Use the image to answer the question.
Parallelogram upper A upper D upper C upper B is graphed on a plane, with diagonal upper A upper C.
In parallelogram ABCD, diagonal AC¯¯¯¯¯¯¯¯ is drawn, and ∠BCA≅∠DAC and ∠BAC≅∠DCA . In order to prove △ABC≅△CDA by the ASA Congruence Theorem, what additional information must be stated and justified?
(1 point)
Responses
AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ by the Triangle Angle Sum Theorem.
Modifying above upper A upper B with bar congruent to Modifying above upper C upper D with bar by the Triangle Angle Sum Theorem.
AC¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.
Modifying above upper A upper C with bar congruent to Modifying above upper A upper C with bar by the Reflexive Property of Congruence.
DA¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.
Modifying above upper D upper A with bar congruent to Modifying above upper B upper C with bar by the Reflexive Property of Congruence.
∠B≅∠D by the Reflexive Property of Congruence.
angle upper B congruent to angle upper D by the Reflexive Property of Congruence.
Question 5
A)
Use the image to answer the question.
Two congruent triangles, upper A upper B upper C and upper B upper C upper D, are mirrored over side upper B upper C on a plane. B both angels B are congruent. Both angels C are congruent.
Based on the markings in the diagram, what additional information must be stated in order to prove △ABC≅△DBC by the ASA Congruence Theorem?
(1 point)
Responses
AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
∠A≅∠D
angle upper A congruent to angle upper D
BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
Answers
Answered by
GPT-4o mini
Here are the answers to the questions provided:
**Question 1:**
To prove △ABC≅△A′′B′′C′′, the correct response showing how the ASA criterion follows from the definition of congruence in terms of rigid motions is:
- **Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across CA′.**
**Question 2:**
The pair of triangles that could be proven congruent by the ASA Congruence Theorem is:
- **Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.**
**Question 3:**
For the transformation indicated by ray AA′, the correct response is:
- **Ray AA′ indicates a reflection.**
**Question 4:**
To prove △ABC≅△CDA by the ASA Congruence Theorem, the additional information that must be stated and justified is:
- **AC¯≅AC¯ by the Reflexive Property of Congruence.**
**Question 5:**
In order to prove △ABC≅△DBC by the ASA Congruence Theorem, the additional information that must be stated is:
- **∠A≅∠D.**
Please let me know if you need further assistance with any specific question!
**Question 1:**
To prove △ABC≅△A′′B′′C′′, the correct response showing how the ASA criterion follows from the definition of congruence in terms of rigid motions is:
- **Rotate △ABC −90 degrees (clockwise) about vertex C, and then reflect △A′B′C′ across CA′.**
**Question 2:**
The pair of triangles that could be proven congruent by the ASA Congruence Theorem is:
- **Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. The sides upper A upper C and upper Q upper S are marked congruent by one tick mark.**
**Question 3:**
For the transformation indicated by ray AA′, the correct response is:
- **Ray AA′ indicates a reflection.**
**Question 4:**
To prove △ABC≅△CDA by the ASA Congruence Theorem, the additional information that must be stated and justified is:
- **AC¯≅AC¯ by the Reflexive Property of Congruence.**
**Question 5:**
In order to prove △ABC≅△DBC by the ASA Congruence Theorem, the additional information that must be stated is:
- **∠A≅∠D.**
Please let me know if you need further assistance with any specific question!
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