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Definition of Similar Figures Practice

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Question
Use the image to answer the question.

2 right triangles are drawn in a coordinate plane where the axes are unlabeled. 1 of the triangles is made up of points upper A, upper B, and upper C, while the other is made up of points upper A prime, upper B prime, and upper C prime.

Triangles ABC
and A′B′C′
both have a 90-degree angle at points B
and B′
; given this information and the image displayed, which criterion proves that the triangles are similar? Enter the number of the correct option.

Option #1: SAS because there are two given sides and an included angle measure of 90 degrees

Option #2: AA because all angles of similar triangles are similar as well

Option #3: SSS because the two given side lengths are proportional

(1 point)
Option #
proves the triangles are similar.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To determine which criterion proves that the triangles are similar, we can analyze the information provided:

  1. Both triangles ( ABC ) and ( A'B'C' ) have a right angle (90 degrees) at points ( B ) and ( B' ). This means that one angle in each triangle is equal (both are 90 degrees).

  2. Since similar triangles share the same angles, if we can show that another corresponding angle is equal, we can establish similarity based on the AA criterion.

From this information, the criterion that can be used to prove that the triangles are similar is:

Option #2: AA because all angles of similar triangles are similar as well.

Thus, the correct answer is:

Option #2 proves the triangles are similar.