Question

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

Explanation:

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

In $\triangle MNO$, we know one angle is $31^{\circ}$ and another is $90^{\circ}$. Using the angle - sum property of a triangle ($\angle M+\angle N+\angle O = 180^{\circ}$), the third angle $\angle MON=180^{\circ}-(90^{\circ}+31^{\circ}) = 59^{\circ}$.

Step2: Find the third angle of $\triangle PNR$

In $\triangle PNR$, we know one angle is $69^{\circ}$ and another is $90^{\circ}$. Using the angle - sum property of a triangle ($\angle P+\angle N+\angle R = 180^{\circ}$), the third angle $\angle NPR=180^{\circ}-(90^{\circ}+69^{\circ}) = 21^{\circ}$.
Since the angles of $\triangle MNO$ ($31^{\circ},90^{\circ},59^{\circ}$) and $\triangle PNR$ ($21^{\circ},90^{\circ},69^{\circ}$) are not equal, the triangles are not similar.

Answer:

$\triangle MNO$ is not similar to $\triangle PNR$.