Question
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.
Answer
4.4
(283 Votes)
Harriet
Veteran · Tutor for 10 years
Answer
#ExplanationIn the context of right triangles, the statement
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,
because the triangles are both right triangles." is incorrect.The measures of sides a and p have no direct relation to the ratio
and
. Therefore, the statement "No,
and
may not be equal because a and p may not be equal." is also incorrect.The measures of
and
do have a direct relation to the ratio
and
. If
and
are equal, then the triangles are similar and the ratios of their corresponding sides are equal. Therefore, the statement "No,
and
may not be equal because the measures of
and
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,
because the triangles are similar." is also correct.#Answer"No,
and
may not be equal because the measures of
and
may not be equal.""Yes,
because the triangles are similar."