Question

criteria for determining triangle similarity include:
a. sss (side-side-side)
b. aa (angle-angle)
c. ssa (side-side-angle)
d. sas (side-angle-side)

Explanation:

• SSS (Side - Side - Side): If the ratios of the corresponding sides of two triangles are equal, the triangles are similar.
• AA (Angle - Angle): If two angles of one triangle are equal to two angles of another triangle, the triangles are similar (since the third angle will also be equal as the sum of angles in a triangle is \(180^{\circ}\)).
• SAS (Side - Angle - Side): If the ratio of two pairs of corresponding sides is equal and the included angles are equal, the triangles are similar.
• SSA (Side - Side - Angle): This is not a valid criterion for triangle similarity. There can be ambiguity (two different triangles can satisfy the SSA condition in some cases).

Answer:

a. SSS (Side - Side - Side), b. AA (Angle - Angle), d. SAS (Side - Angle - Side)