Question

△mno and △opq are shown below.which statement is true?△mno is similar to △opq.△mno is not similar to △opq.there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate the third angle of $\triangle MNO$

In $\triangle MNO$, we know that $\angle N = 90^{\circ}$ and $\angle MON=59^{\circ}$. Using the angle - sum property of a triangle ($\angle N+\angle MON+\angle OMN = 180^{\circ}$), we can find $\angle OMN$.

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Step2: Check the similarity of triangles using AA (Angle - Angle) criterion

In $\triangle MNO$ and $\triangle OPQ$:

• $\angle N=\angle P = 90^{\circ}$ (right angles)
• $\angle OMN=\angle POQ = 31^{\circ}$ (from Step 1 and given)

By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

$\triangle MNO$ is similar to $\triangle OPQ$.