Which of the following is NOT a way you can show that triangles are similar?
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A. AAA similarity
B. SAS similarity
C. SSA similarity
D. SSS similarity
To determine which of the given options is NOT a way to show that triangles are similar, we have to understand the criteria for triangle similarity.
In mathematics, two triangles are considered similar if their corresponding angles are equal and their corresponding sides are in proportion. Let's evaluate each option to determine which one does not align with the criteria for triangle similarity:
A. AAA similarity:
AAA stands for Angle-Angle-Angle similarity. It means that if the three angles of one triangle are congruent (equal) to the three angles of another triangle, then the two triangles are similar. This option aligns with the criteria for triangle similarity.
B. SAS similarity:
SAS stands for Side-Angle-Side similarity. It states that if two pairs of corresponding sides of two triangles are in proportion (the ratios between the corresponding sides are equal), and the included angles (the angles between the two pairs of sides) are congruent, then the triangles are similar. This option aligns with the criteria for triangle similarity.
C. SSA similarity:
SSA stands for Side-Side-Angle similarity. SSA similarity is not a valid way to prove that triangles are similar. If two pairs of corresponding sides of two triangles are in proportion, and the included angle (angle between the two pairs of sides) is congruent, it does not guarantee that the two triangles are similar. This option does not align with the criteria for triangle similarity.
D. SSS similarity:
SSS stands for Side-Side-Side similarity. It states that if the corresponding sides of two triangles are in proportion (the ratios between the corresponding sides are equal), then the triangles are similar. This option aligns with the criteria for triangle similarity.
Based on the above analysis, the correct answer is C. SSA similarity, as it does not align with the criteria for triangle similarity.