Chapter 9

Draw two similar triangles whose scale factor is \(\frac{1}{3}\). Justify your answer.

Estimate each square root to the nearest integer. Do not use a calculator. $$ -\sqrt{54} $$

Classify each angle as acute, obtuse, right, or straight. $$140^{\circ}$$

Replace each \(\odot\) with \(<,>,\) or \(=\) to make a true statement. $$-3.3 \odot-\sqrt{10}$$

Writing in Math How is the Distance Formula related to the Pythagorean Theorem? Include a comparison of the expressions \(\left(x_{2}-x_{1}\right)\) and \(\left(y_{2}-y_{1}\right)\) to the lengths of the legs of a right triangle.

FIND THE ERROR Carla and Tony are finding the length of \(\overline{A B}\) where \(\triangle A B C \sim \triangle D E F, B C=16\) feet, \(E F=12\) feet, and \(D E=18\) feet. Who is correct? Explain your reasoning. $$\begin{aligned}&\begin{array}{l}\text { Carla } \\\\\frac{16}{18}=\frac{12}{x}\end{array}\\\&x=13.5 \mathrm{ft}\end{aligned}$$ $$\begin{aligned}&\begin{array}{r}\text { Tony } \\\\\frac{16}{12}=\frac{x}{18}\end{array}\\\&x=24 \mathrm{ft}\end{aligned}$$

A The floor exercise mat measures 40 feet by 40 feet. Find the measure of the diagonal.

Estimate each square root to the nearest integer. Do not use a calculator. $$-\sqrt{125}$$

Classify each angle as acute, obtuse, right, or straight. $$38^{\circ}$$

Replace each \(\odot\) with \(<,>,\) or \(=\) to make a true statement. $$-\sqrt{18} \odot-4 \frac{3}{8}$$

Which expression shows how to find the distance between points \(M\) and \(N ?\)A \(\sqrt{(2-5)^{2}+(3-3)^{2}}\) B \(\sqrt{[2-(-5)]^{2}+[3-(-3)]^{2}}\) c \(\sqrt{12-\left.(-5)\right|^{2}+(3-3)^{2}}\) D \(\sqrt{(3-2)^{2}+[3-(-5)]^{2}}\)

CHALLENGE Triangle \(A B C\) has side lengths of 3 inches, 5 inches, and 6 inches. Triangle \(D E F\) has side lengths 4 inches, 6 inches, and 8 inches. Determine whether \(\triangle A B C \sim \triangle D E F .\) Explain.

The size of a flat-screen television is determined by the length of the diagonal of the screen. If a 35 -inch television screen is 26 inches long, what is its height to the nearest inch?

Estimate each square root to the nearest integer. Do not use a calculator. $$\pm \sqrt{200}$$

Classify each angle as acute, obtuse, right, or straight. $$127^{\circ}$$

Replace each \(\odot\) with \(<,>,\) or \(=\) to make a true statement. $$1 \frac{1}{2} \odot \sqrt{2.25}$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=8.1, b=3.5, c=? \quad$$

Writing in Math Suppose you have two triangles. Triangle \(A\) is similar to triangle \(B,\) and the measures of the sides of triangle \(A\) are less than the measures of the sides of triangle \(B\). The scale factor is \(0.25 .\) Which is the original triangle? Explain.

Estimate each square root to the nearest integer. Do not use a calculator. $$\pm \sqrt{396}$$

What type of angle is formed by the hands on a clock at \(6: 00 ?\)

Replace each \(\odot\) with \(<,>,\) or \(=\) to make a true statement. $$-\sqrt{6.25} \odot-\frac{5}{2}$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=10.4, b=16.9, c=?$$

Order each set of numbers from least to greatest. $$5 \frac{1}{4}, 2 . \overline{1}, \sqrt{4}, \frac{6}{5}$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=27, b=?, c=61$$

Order each set of numbers from least to greatest. $$4 . \overline{23}, 4 \frac{2}{3}, \sqrt{18}, \sqrt{16}$$

Find the distance between each pair of points. Round to the nearest tenth, if necessary. (Lesson \(9-5\) ) $$S(2,3), T(0,6)$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=?, b=73, c=82$$

Order each set of numbers from greatest to least. $$-10,-10 \frac{1}{2},-1.05,-\sqrt{105}$$

ALGEBRA The measures of the angles of a triangle are in the ratio \(1: 4: 5 .\) Find the measure of each angle. (lesson \(9-3\) )

Find the distance between each pair of points. Round to the nearest tenth, if necessary. (Lesson \(9-5\) ) $$E(-1,1), F(3,-2)$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=?, b=\sqrt{123}=, c=22$$

The number \(\sqrt{54}\) lies between which two consecutive whole numbers?

Order each set of numbers from greatest to least. $$-\sqrt{14},-4 \frac{1}{10},-\frac{17}{4},-3.8$$

What number is \(56 \%\) of \(85 ?\) ( lesson \(6-8\) )

Find the distance between each pair of points. Round to the nearest tenth, if necessary. (Lesson \(9-5\) ) $$W(4,-6), V(-3,-5)$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. $$a=\sqrt{177}=, b=?, c=31$$

Which is greater, \(\sqrt{65}\) or \(9 ?\) Explain your reasoning.

Solve each equation. Round to the nearest tenth, if necessary. $$a^{2}=49$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. (lesson \(9-4\) ) $$a=10, b=15, c=?$$

Which is less, 11 or \(\sqrt{120} ?\) Explain your reasoning.

Solve each equation. Round to the nearest tenth, if necessary. $$300=h^{2}$$

Solve each proportion. $$\frac{4}{16}=\frac{7}{x}$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. (lesson \(9-4\) ) $$a=8, b=?, c=34$$

Sketch each triangle. If it is not possible to sketch the triangle, write not possible. acute scalene

Solve each equation. Round to the nearest tenth, if necessary. $$y^{2}=22$$

Solve each proportion. $$\frac{a}{15}=\frac{12}{60}$$

If \(c\) is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. (lesson \(9-4\) ) $$a=?, b=27, c=82$$

Order \(\sqrt{77},-8,-\sqrt{83}, 9,-10,-\sqrt{76}, \sqrt{65}\) from least to greatest.

Sketch each triangle. If it is not possible to sketch the triangle, write not possible. obtuse and not scalene

Solve each equation. Round to the nearest tenth, if necessary. $$0.0058=k^{2}$$