91Ó°ÊÓ

For the \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle shown, suppose that \(A B=a \sqrt{2} .\) Find: a) \(A C\) b) \(B C\) (GRAPH CANT COPY)

In Exercises 5 to 22 , find the missing lengths. Give your answers in both simplest radical form and as approximations to two decimal places. Given: Right \(\triangle X Y Z\) with \(\mathrm{m} \angle X=45^{\circ}\) and \(X Z=8\) Find: \(\quad Y Z\) and \(X Y\) (GRAPH CANT COPY)

In Exercises 5 to 22 , find the missing lengths. Give your answers in both simplest radical form and as approximations to two decimal places. Given: Right \(\triangle X Y Z\) with \(\overline{X Z} \cong \overline{Y Z}\) and \(X Y=10 \sqrt{2}\) Find: \(\quad X Z\) and \(Y Z\) (GRAPH CANT COPY)

Find the value of \(x\) in each proportion. a) \(\frac{x+1}{2}=\frac{7}{x-1}\) b) \(\frac{x+1}{3}=\frac{5}{x-2}\)

Quadrilateral \(A B C D \sim\) quadrilateral \(H J K L\). If \(\mathrm{m} \angle A=\mathrm{m} \angle K=70^{\circ},\) and \(\mathrm{m} \angle B=110^{\circ},\) what types of quadrilaterals are \(A B C D\) and \(H J K L ?\)

If \(1 \mathrm{kg}\) equals \(2.2 \mathrm{Ib},\) use a proportion to convert 12 pounds to kilograms.

An isosceles right triangle has a hypotenuse of length \(10 \mathrm{cm} .\) How long is each leg?

A blueprint represents the 72 -ft length of a building by a line segment of length 6 in. What length on the blueprint would be used to represent the height of this 30 -ft-tall building?

Given: \( \triangle R S T,\) with \(\overleftrightarrow{X Y}\|\overline{R T}, \overleftrightarrow{Y Z}\| \overline{R S}\) Prove: \(\frac{R X}{X S}=\frac{Z T}{R Z}\).

On a blueprint, a 1 -in. scale corresponds to 3 ft. To show a room with actual dimensions 12 ft wide by 14 ft long, what dimensions should be shown on the blueprint?