91Ó°ÊÓ

Given: \(\quad\) Right \(\triangle D E F\) with \(\mathrm{m} \angle E=60^{\circ}\) and \(F D=12 \sqrt{3}\) Find: \(\quad D E\) and \(F E\) (GRAPH CANT COPY)

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

Determine whether each triple \((a, b, c)\) is a Pythagorean triple. a) \((8,15,17)\) c) \((6,8,10)\) b) \((10,13,19)\) d) \((11,17,20)\)

Given: \(\quad\) Right \(\triangle D E F\) with \(\mathrm{m} \angle E=2 \cdot \mathrm{m} \angle F\) and \(E F=12 \sqrt{3}\) Find: \(\quad D E\) and \(D F\) (GRAPH CANT COPY)

Determine the type of triangle represented if the lengths of its sides are: a) \(a=4, b=3,\) and \(c=5\) b) \(a=4, b=5,\) and \(c=6\) c) \(a=2, b=\sqrt{3},\) and \(c=\sqrt{7}\) d) \(a=3, b=8,\) and \(c=15\)

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

Determine the type of triangle represented if the lengths of its sides are: a) \(a=1.5, b=2,\) and \(c=2.5\) b) \(a=20, b=21,\) and \(c=29\) c) \(a=10, b=12,\) and \(c=16\) d) \(a=5, b=7,\) and \(c=9\)

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

Given: \(\overrightarrow{R W}\) bisects \(\angle S R T\) Do the following equalities hold? a) \(\frac{R S}{S W}=\frac{R T}{W T}\) b) \(\mathrm{m} \angle S=\mathrm{m} \angle T\)

Given: \(\begin{array}{ll} \overrightarrow{U T} \text { bisects } \angle W U V, W U=8, U V=12 \\ W T=6\end{array}\) Find: \(T V\).