Question

question 5 of 10 based only on the information given in the diagram, it is guaranteed that △rst～△uvw. a. true b. false

Explanation:

Step1: Find third - angle of first triangle

In $\triangle RST$, one angle is $72^{\circ}$ and another is $90^{\circ}$. Using the angle - sum property of a triangle ($180^{\circ}$ in a triangle), the third angle $\angle S=180-(90 + 72)=18^{\circ}$.

Step2: Compare angles

In $\triangle RST$, angles are $72^{\circ},90^{\circ},18^{\circ}$. In $\triangle UVW$, angles are $18^{\circ},90^{\circ},72^{\circ}$. Since the corresponding angles of $\triangle RST$ and $\triangle UVW$ are equal, by the AA (angle - angle) similarity criterion, $\triangle RST\sim\triangle UVW$.

Answer:

A. True