91Ó°ÊÓ

In Exercises \(13-16,\) two polygons are similar. The perimeter of one polygon and the ratio of the corresponding side lengths are given. Find the perimeter of the other polygon. perimeter of smaller polygon: \(66 \mathrm{ft} ;\) ratio: \(\frac{3}{4}\)

In Exercises \(13-16,\) two polygons are similar. The perimeter of one polygon and the ratio of the corresponding side lengths are given. Find the perimeter of the other polygon. perimeter of larger polygon: 120 yd; ratio: \(\frac{1}{6}\)

MODELING WITH MATHEMATICS A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45?feet. Find the perimeters of an NCAA court and of the new court in the school.

MODELING WITH MATHEMATICS Your family has decided to put a rectangular patio in your backyard, similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio.

MATHEMATICAL CONNECTIONS Explain how you can use similar triangles to show that any two points on a line can be used to ind its slope.

Prove the Converse of the Triangle Proportionality Theorem (Theorem 8.7). Given \(\frac{Z Y}{Y W}=\frac{Z X}{X V}\) Prove \(\overline{Y X}, \overline{W V}\)

THOUGHT PROVOKING Decide whether each is a valid method of showing that two quadrilaterals are similar. Justify your answer. a. \(A A A\) b. AAAA

Are any two right triangles similar? Explain.

PROOF Without using corresponding lengths in similar polygons, prove that the ratio of two corresponding angle bisectors in similar triangles is equal to the scale factor.

PROOF Prove that if the lengths of two sides of a triangle are a and \(b,\) respectively, then the lengths of the corresponding altitudes to those sides are in the ratio \(\frac{b}{a}\)