Question

emily and her classmates are discussing the triangles below. emily says they are similar based on aa similarity. sarah says they are similar based on ssa similarity. elinor says they are similar based on sas similarly. who is correct?

Explanation:

Step1: Check for AA similarity

Both triangles are right - angled (one right angle each).
For the first triangle with sides \(8\) and \(6\), and the second with sides \(4\) and \(3\).
The ratio of the sides is \(\frac{8}{4}=\frac{6}{3} = 2\).
Since the triangles are right - angled (one pair of equal angles) and the sides are in proportion (which implies the other non - right angles are equal as well).

Step2: Check SSA and SAS

SSA is not a valid similarity criterion for triangles.
For SAS similarity, we need two sides in proportion and the included angle equal. Here, we have two pairs of sides in proportion (\(\frac{8}{4}=\frac{6}{3}\)), but the right angle is not the included angle between the sides \(8\) and \(6\) (or \(4\) and \(3\)) in the context of SAS similarity for these triangles.

Answer:

Emily is correct.