Question
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
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.
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.
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.
Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis.
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
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.
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.
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.
Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis.
Answers
GPT-4o mini
To determine that the dilated triangle A′B′C′ is similar to triangle ABC using the AA criteria, we can consider the following response:
**Find the angle measures of the original triangle (ABC) and the dilated triangle (A′B′C′), then compare the angle measures. If two angles of one triangle are equal to two angles of the other triangle, then the triangles are similar by the AA criterion.**
This response highlights that, for similarity through the AA criterion, it is essential to establish that the angles of the triangles are congruent. Since the triangles undergo a dilation, their angles remain the same while their side lengths change proportionally, confirming that the triangles are similar.
**Final Answer: Find the angle measures of the original triangle and the dilated triangle, then compare the angle measures.**
**Find the angle measures of the original triangle (ABC) and the dilated triangle (A′B′C′), then compare the angle measures. If two angles of one triangle are equal to two angles of the other triangle, then the triangles are similar by the AA criterion.**
This response highlights that, for similarity through the AA criterion, it is essential to establish that the angles of the triangles are congruent. Since the triangles undergo a dilation, their angles remain the same while their side lengths change proportionally, confirming that the triangles are similar.
**Final Answer: Find the angle measures of the original triangle and the dilated triangle, then compare the angle measures.**