Question

in the figure, ∠qpr = ∠qmn. which criterion can be used to show △qmn ~ △qpr?

Explanation:

Step1: Identify common angle

$\angle Q$ is common to both $\triangle QMN$ and $\triangle QPR$.

Step2: Given equal - angle condition

Given $\angle QMN=\angle QPR$.

Step3: Apply AA (Angle - Angle) similarity criterion

Two angles of $\triangle QMN$ are equal to two angles of $\triangle QPR$. By AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the two triangles are similar.

Answer:

AA (Angle - Angle) similarity criterion can be used to show $\triangle QMN\sim\triangle QPR$.