Question

explain why triangle rst is similar to triangle tyz.

Explanation:

Both $\triangle RST$ and $\triangle TYZ$ are right - angled triangles. The angles $\angle RST=\angle TYZ = 90^{\circ}$. Also, the lines containing the hypotenuses of the two triangles are part of the same straight line, so the non - right angles in the two triangles are equal (corresponding angles). By the AA (angle - angle) similarity criterion for triangles, if two angles of one triangle are equal to two angles of another triangle, the two triangles are similar.

Answer:

$\triangle RST$ is similar to $\triangle TYZ$ by the AA similarity criterion since $\angle RST=\angle TYZ = 90^{\circ}$ and the non - right angles are equal as they are corresponding angles formed by the same straight line containing the hypotenuses.