Question

are these triangles similar?
yes
no
write a similarity statement
△ ≈ △

Explanation:

Step1: Find the third angle of each triangle

For \(\triangle KIJ\), using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle). Let the third angle be \(x\). Then \(x + 93^{\circ}+32^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(93^{\circ}+32^{\circ})=55^{\circ}\).
For \(\triangle TRS\), using the angle - sum property of a triangle. Let the third angle be \(y\). Then \(y + 32^{\circ}+93^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-(93^{\circ}+32^{\circ})=55^{\circ}\).

Step2: Check for similarity

Since \(\angle I = \angle R = 93^{\circ}\), \(\angle J=\angle T = 32^{\circ}\), and \(\angle K=\angle S=55^{\circ}\), by the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), the triangles are similar.

Step3: Write the similarity statement

The order of the letters corresponds to the equal angles. So \(\triangle KIJ\sim\triangle SRT\) (because \(\angle K\) corresponds to \(\angle S\), \(\angle I\) corresponds to \(\angle R\), and \(\angle J\) corresponds to \(\angle T\))

Answer:

yes; \(\triangle KIJ\sim\triangle SRT\)