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Question 1

A)Explain how the SAS criterion can be used to prove similarity in two triangles.(1 point)
Responses

If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.
If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.

If at least two angles of the triangles are given and are the same, then the triangles are similar.
If at least two angles of the triangles are given and are the same, then the triangles are similar.

If given a scale factor, you can determine if triangles are similar.
If given a scale factor, you can determine if triangles are similar.

If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar.
If all three side lengths are given and proportional to one another, resulting in the same scale factor, then the triangles are similar.
Question 2
A)
Use the image to answer the question.

A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Triangles upper A upper B upper C and upper A prime upper B prime upper C prime are drawn in the system.

How can a similarity transformation be used to determine that the AA criterion proves the dilated triangle A′B′C′ is similar to triangle ABC?

(1 point)
Responses

Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis.
Reflect the triangle across the x -axis and check for symmetry among the triangles with respect to the x -axis.

Center the original triangle inside the dilated triangle and see if the side lengths are congruent by using the scale factor.
Center the original triangle inside the dilated triangle and see if the side lengths are congruent by using the scale factor.

Translate the dilated triangle so one of its angles exactly matches the corresponding angle in the original triangle; repeat using a different pair of angles.
Translate the dilated triangle so one of its angles exactly matches the corresponding angle in the original triangle; repeat using a different pair of angles.

Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.
Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.
Question 3
A)Two triangles are sketched on a coordinate plane using a dilation of 2, sharing the same center ordered pair at the origin. One triangle has angle measures of 34 degrees and 80 degrees. Using the AA criterion, what would be the two corresponding angles of the dilated triangle?(1 point)
Responses

17 degrees and 40 degrees
17 degrees and 40 degrees

68 degrees and 160 degrees
68 degrees and 160 degrees

34 degrees and 80 degrees
34 degrees and 80 degrees

44 degrees and 70 degrees
44 degrees and 70 degrees
Question 4
A)How does a dilation transformation compare to translations, rotations, and reflections?(1 point)
Responses

All transformations change the size and shape of figures.
All transformations change the size and shape of figures.

Dilation transformations make figures larger; translations shrink figures.
Dilation transformations make figures larger; translations shrink figures.

Dilation transformations are the only ones that do not maintain the same side lengths.
Dilation transformations are the only ones that do not maintain the same side lengths.

All transformations move figures across the coordinate plane.
All transformations move figures across the coordinate plane.
Question 5
A)When a figure undergoes a reflection, it changes(1 point)
Responses

both position and size.
both position and size.

both position and orientation.
both position and orientation.

orientation only.

1 answer

Here are the responses based on the questions provided:

Question 1 A) Explain how the SAS criterion can be used to prove similarity in two triangles.
Response: If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.

Question 2 A) How can a similarity transformation be used to determine that the AA criterion proves the dilated triangle A′B′C′ is similar to triangle ABC?
Response: Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.

Question 3 A) Using the AA criterion, what would be the two corresponding angles of the dilated triangle if the original triangle has angles of 34 degrees and 80 degrees?
Response: 34 degrees and 80 degrees.

Question 4 A) How does a dilation transformation compare to translations, rotations, and reflections?
Response: Dilation transformations are the only ones that do not maintain the same side lengths.

Question 5 A) When a figure undergoes a reflection, it changes:
Response: both position and orientation.

Feel free to ask if you need more help or clarification!