Question

which rule explains why these triangles are similar?

(image of two triangles: triangle ijk with angle at i being 91° and a marked angle at j; triangle tus with angle at s being 91° and a marked angle at u)

options:

• sss
• sas
• aa
• none of the above; the triangles cannot be proven similar

Explanation:

We are given two triangles: $\triangle IKJ$ has $\angle I = 91^\circ$ and marked $\angle J$, while $\triangle TUS$ has $\angle S = 91^\circ$ and marked $\angle U$. The marked angles at $J$ and $U$ are congruent. This gives us two pairs of corresponding congruent angles: $\angle I \cong \angle S$ and $\angle J \cong \angle U$. By the AA (Angle-Angle) similarity criterion, if two pairs of corresponding angles of two triangles are congruent, the triangles are similar.

Answer:

AA