Triangles JBE and AJR differ in angle measurements (80° vs 70°) and lack proportional side lengths, failing both AA and SSS similarity postulates. They are not similar.
Triangles JBE and AJR are not similar. Here's why:
Corresponding Angles: While both triangles share a right angle at B and at J, the other two angles are not congruent. Angle JBE measures 80 degrees, while angle AJR measures 70 degrees.
Proportional Side Lengths: Even though some corresponding side lengths have close values (e.g., JE in JBE is 21.3 units and AJ in AJR is 18 units), they are not proportional. For example, the ratio of JE to AJ is not equal to the ratio of BE to JR (21.3/18 ≠ 25.4/24).
Therefore, based on the AA Similarity postulate (two triangles are similar if they have two corresponding angles that are congruent) and the SSS Similarity postulate (two triangles are similar if their corresponding side lengths are proportional), triangles JBE and AJR are not similar.
Complete question below:
Determine if the triangles are similar. If they are similar, give the scale factor. If they are not similar, then write NONE.