The diagram shows two right triangles. Is it true that (b)/(c) and (q)/(r) must be equal? No, (b)/(c) and (q)/(r) may not be equal because a and p may not be equal. No, (b)/(c) and (q)/(r) may not be equal because the measures of angle B and angle Q may not be equal. Yes, (b)/(c)=(q)/(r) because the triangles are both right triangles. Yes, (b)/(c)=(q)/(r) because the triangles are similar.

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The diagram shows two right triangles. Is it true that (b)/(c) and (q)/(r) must be equal? No, (b)/(c) and (q)/(r) may not be equal because a and p may not be equal. No, (b)/(c) and (q)/(r) may not be equal because the measures of angle B and angle Q may not be equal. Yes, (b)/(c)=(q)/(r) because the triangles are both right triangles. Yes, (b)/(c)=(q)/(r) because the triangles are similar.

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#Explanation In the context of right triangles, the statement $\frac {b}{c}=\frac {q}{r}$ is referring to the ratios of corresponding sides of the triangles. This ratio is equal if and only if the triangles are similar. Two triangles are similar if their corresponding angles are equal. In right triangles, one angle is always 90 degrees. However, this does not guarantee that the other two angles are equal in measure, and thus does not guarantee similarity of the triangles. Therefore, the statement "Yes, $\frac {b}{c}=\frac {q}{r}$ because the triangles are both right triangles." is incorrect. The measures of sides a and p have no direct relation to the ratio $\frac {b}{c}$ and $\frac {q}{r}$. Therefore, the statement "No, $\frac {b}{c}$ and $\frac {q}{r}$ may not be equal because a and p may not be equal." is also incorrect. The measures of $\angle B$ and $\angle Q$ do have a direct relation to the ratio $\frac {b}{c}$ and $\frac {q}{r}$. If $\angle B$ and $\angle Q$ are equal, then the triangles are similar and the ratios of their corresponding sides are equal. Therefore, the statement "No, $\frac {b}{c}$ and $\frac {q}{r}$ may not be equal because the measures of $\angle B$ and $\angle Q$ may not be equal." is correct. Finally, if the triangles are similar, then the ratios of their corresponding sides are equal. Therefore, the statement "Yes, $\frac {b}{c}=\frac {q}{r}$ because the triangles are similar." is also correct. #Answer "No, $\frac {b}{c}$ and $\frac {q}{r}$ may not be equal because the measures of $\angle B$ and $\angle Q$ may not be equal." "Yes, $\frac {b}{c}=\frac {q}{r}$ because the triangles are similar."

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