?Determine whether each statement is true or false. If the statement is false, replace

Use the number line to find each measure. \(AD\) Equation Transcription: Text Transcription: AD

Use the number line to find each measure. \(DE\) Equation Transcription: Text Transcription: DE

Use the number line to find each measure. \(DH\) Equation Transcription: Text Transcription: DH

Use the number line to find each measure. \(AC\) Equation Transcription: Text Transcription: AC

Use the number line to find each measure. \(BF\) Equation Transcription: Text Transcription: BF

Use the number line to find each measure. \(GH\) Equation Transcription: Text Transcription: GH

Solve each inequality. Graph the solution on a number line. \(n+7<12\) Equation Transcription: Text Transcription: n + 7 < 12

Solve each inequality. Graph the solution on a number line. \(14+p<32\) Equation Transcription: Text Transcription: 14 + p < 32

Solve each inequality. Graph the solution on a number line. \(55+r<90\) Equation Transcription: Text Transcription: 55 + r < 90

Solve each inequality. Graph the solution on a number line. \(18>d-4\) Equation Transcription: Text Transcription: 18 > d - 4

Solve each inequality. Graph the solution on a number line. \(w-15>15\) Equation Transcription: Text Transcription: w - 15 > 15

Solve each inequality. Graph the solution on a number line. \(22-t>15\) Equation Transcription: Text Transcription: 22 - t > 15

Refer to the figure. Name two pairs of adjacent angles.

Refer to the figure. Name a pair of supplementary angles.

Refer to the figure. . Find the measure of \(\angle C F B\). Equation Transcription: Text Transcription: angle CFB

Use uncooked linguine to investigate three different triangles. First, break a piece of linguine into two \(3\)-inch lengths. a. Using a protractor as a guide, place the two \(3\)-inch pieces of linguine together to form a \(30^{\circ}\) angle. Break a third piece of linguine so its length forms a triangle with the first two pieces. Trace around the triangle and label it Triangle \(1\). Measure and record the length of the third side of the triangle. b. Using a protractor, place the two \(3\)-inch pieces of linguine together to form a \(60^{\circ}\) angle. Break another piece of linguine and use it to form a triangle with the first two pieces. Trace around the triangle and label it Triangle \(2\). Measure and record the length of the third side of your triangle. c. Using a protractor, place the two \(3\)-inch pieces of linguine together to form a \(90^{\circ}\) angle. Break another piece of linguine and use it to form a triangle with the first two pieces. Trace around the triangle and label it Triangle \(3\). Measure and record the length of the third side of the triangle. d. As the angle opposite the third side of the triangle increases, what happens to the measure of the third side? Equipment Transcription: Text Transcription: 3 30 degrees 1 60 degrees 2 90 degrees

Break four pieces of linguine so that you have the following lengths: \(2\) inches, \(3\) inches, \(4\) inches, and \(5\) inches. a. Use a protractor to form a \(40^{\circ}\) angle between the \(2\)-inch piece and the \(3\)-inch piece as shown at the right. Break a third piece of linguine to form a triangle. Trace around the triangle and label it Triangle \(4\). Record the measure of angle \(1\) shown in the figure. b. In the linguine triangle from Step \(2a\), replace the \(3\)-inch piece with the \(4\)-inch piece. Keep the angle measure between the pieces \(40^{\circ}\). Break a third piece of linguine to form a triangle. Trace around the triangle and label it Triangle \(5\). Record the measure of angle \(1\). c. In the linguine triangle from Step \(2b\), replace the \(4\)-inch piece with the \(5\)-inch piece. Keep the angle measure between the pieces \(40^{\circ}\). Break a third piece of linguine to form a triangle. Trace around the triangle and label it Triangle \(6\). Record the measure of angle \(1\). d. In the three triangles that you formed, each contained a \(40^{\circ}\) angle. One side remained \(2\) inches long, but the other side adjacent to the \(40^{\circ}\) angle increased from \(3\) to \(4\) to \(5\) inches. As that side increased in length, what happened to the measure of angle \(1\)? Equation Transcription: Text Transcription: 2 3 4 5 40 degrees 1 2a 2b 6

Replace each with <, >, or = to make a true sentence. \(JA\) \(ST\) Equation Transcription: Text Transcription: JA ST

Replace each with <, >, or = to make a true sentence. \(m \angle J S T\) \(m \angle S T N\) Equation Transcription: Text Transcription: m angle JST m angle STN

Find the measure of each angle. \(\angle 2\) Equation Transcription: Text Transcription: angle 2

Find the measure of each angle. \(\angle D\) Equation Transcription: Text Transcription: angle D

Perth, Darwin, and Sydney are three cities in Australia. Which two of the cities are the farthest apart?

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. The expression \(4 y-9 \leq 5\) is an example of an equation. Equation Transcription: Text Transcription: 4y - 9 leq 5

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. In Figure 1, \(\angle 3\), \(\angle 5\), and \(\angle 8\) are exterior angles. Equation Transcription: Text Transcription: 1 angle 3 angle 5 angle 8

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. \(C M \geq B Q\) means the length of \(\overline{C M}\) is less than the length of \(\overline{B Q}\). Equation Transcription: Text Transcription: CM geq BQ overline CM overline BQ

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. A remote interior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle.

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. In Figure \(1\), \(m \angle 7=m \angle 5+m \angle 8\) by the Interior Angle Theorem. Equation Transcription: Text Transcription: 1 m angle 7 = m angle 5 + m angle 8

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. \(m \angle Z<m \angle Y\) means the measure of angle \(Z\) is less than or equal to the measure of angle \(Y\). Equation Transcription: Text Transcription: m angle Z < m angle Y Z Y

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. In Figure \(1\), the exterior angles at \(K\) are \(\angle 6\), \(\angle 9\), and \(\angle B K D\). Equation Transcription: Text Transcription: 1 K angle 6 angle 9 angle BKD

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. In Figure \(2\), \(E F+F G\) is equal to \(EG\). Equation Transcription: Text Transcription: 2 EF + FG EG

Determine whether each statement is true or false. If the statement is false, replace the underlined word or phrase to make it true. In Figure \(2\), if \(F G=5\) and \(E F=9\), a possible measure for \(\overline{E G}\) is \(13.9\). Equation Transcription: Text Transcription: 2 FG = 5 EF = 9 overline EG 13.9

Replace each with <, >, or = to make a true sentence. \(m \angle F R V\) \(m \angle F R M\) Equation Transcription: Text Transcription: m angle FRV m angle FRM

Replace each with <, >, or = to make a true sentence. \(JR\) \(RF\) Equation Transcription: Text Transcription: JR RF

Replace each with <, >, or = to make a true sentence. \(FV\) \(FM\) Equation Transcription: Text Transcription: FV FM

Replace each with <, >, or = to make a true sentence. \(m \angle J R V\) \(m \angle M R F\) Equation Transcription: Text Transcription: m angle JRV m angle MRF

Determine if each statement is true or false. \(F M \neq J R\) Equation Transcription: Text Transcription: FM neq JR

Determine if each statement is true or false. \(m \angle J R F \geq m \angle V R J\) Equation Transcription: Text Transcription: m angle JRF geq m angle VRJ

Name the angles. an exterior angle of \(\triangle Q A J\) Equation Transcription: Text Transcription: triangle QAJ

Name the angles. all interior angles of \(\triangle Z A Q\) Equation Transcription: Text Transcription: triangle ZAQ

Name the angles. a remote interior angle of \(\triangle Q Z J\) with respect to \(\angle 1\) Equation Transcription: Text Transcription: triangle QZJ angle 1

Name the angles. a remote interior angle of \(\triangle Z A Q\) with respect to \(\angle 2\) Equation Transcription: Text Transcription: triangle ZAQ angle 2

Find the measure of each angle. \(m \angle P H F\) Equation Transcription: Text Transcription: m angle PHF

Find the measure of each angle. \(m \angle R Y K\) Equation Transcription: Text Transcription: m angle RYK

Replace with <, >, or = to make a true sentence. \(m \angle E\) \(108\) Equation Transcription: Text Transcription: m angle E 108

Find the value of \(x\). Equation Transcription: Text Transcription: x

Find \(m \angle B\). Equation Transcription: Text Transcription: m angle B

Find \(m \angle E\). Equation Transcription: Text Transcription: m angle E

List the angles in order from least to greatest measure.

List the angles in order from least to greatest measure.

Identify the side with the greatest measure.

Identify the side with the greatest measure.

Determine if the three numbers can be measures of the sides of a triangle. Write yes or no. Explain. \(12, 5, 13\) Equation Transcription: Text Transcription: 12,5, 13

Determine if the three numbers can be measures of the sides of a triangle. Write yes or no. Explain. \(27, 11, 39\) Equation Transcription: Text Transcription: 27, 11, 39

Determine if the three numbers can be measures of the sides of a triangle. Write yes or no. Explain. \(15, 45, 60\) Equation Transcription: Text Transcription: 15, 45, 60

If two sides of a triangle have the following measures, find the range of possible measures for the third side. \(2, 9\) Equation Transcription: Text Transcription: 2, 9

If two sides of a triangle have the following measures, find the range of possible measures for the third side. \(10, 30\) Equation Transcription: Text Transcription: 10, 30

If two sides of a triangle have the following measures, find the range of possible measures for the third side. \(34, 18\) Equation Transcription: Text Transcription: 34, 18

The Underground Railroad used quilts as coded directions. In the quilt block shown below, the right triangles symbolize flying geese, a message to follow these birds north to Canada. If \(m \angle F L G=135\) and \(m \angle L S G=6 x-18\), find the value of \(x\). Equation Transcription: Text Transcription: m angle FLG = 135 m angle LSG = 6x - 18 x

A theater has spotlights that move along a track in the ceiling \(16\) feet above the stage. The lights maintain their desired intensity for up to \(30\) feet. One light is originally positioned directly over center stage \(C\). At what distance \(d\) from \(C\) will the light begin to lose its desired intensity? Equation Transcription: Text Transcription: 16 30 C d

True or false: \(TA = KT\). Explain. Equation Transcription: Text Transcription: TA = KT

Replace each with <, >, or = to make a true sentence. \(BK\) \(JK\) Equation Transcription: Text Transcription: BK JK

Replace each with <, >, or = to make a true sentence. \(m \angle D J K\) \(m \angle B D K\) Equation Transcription: Text Transcription: m angle DJK m angle BDK

Replace each with <, >, or = to make a true sentence. \(m \angle B J D\) \(m \angle D K F\) Equation Transcription: Text Transcription: m angle BJD m angle DKF

Replace each with <, >, or = to make a true sentence. \(JF\) \(DF\) Equation Transcription: Text Transcription: JF DF

Replace each with <, >, or = to make a true sentence. \(BD\) \(KF\) Equation Transcription: Text Transcription: BD KF

Replace each with <, >, or = to make a true sentence. \(m \angle J D F\) \(m \angle F D K\) Equation Transcription: Text Transcription: m angle JDF m angle FDK

Determine if each statement is true or false. \(m \angle K F D>m \angle J K D\) Equation Transcription: Text Transcription: m angle KFD > m angle JKD

Determine if each statement is true or false. \(B K \geq D F\) Equation Transcription: Text Transcription: BK geq DF

Determine if each statement is true or false. \(m \angle B D F \ngeq m \angle D K F\) Equation Transcription: ? Text Transcription: m angle BDF ngeq m angle DKF

Determine if each statement is true or false. \(J F \neq B D\) Equation Transcription: Text Transcription: JF neq BD

Name all interior angles of \(\triangle N L E\). Equation Transcription: Text Transcription: triangle NLE

Name an exterior angle of \(\triangle K N C\). Equation Transcription: Text Transcription: triangle KNC

Name a remote interior angle of \(triangle K R E\) with respect to \(\angle K R L\). Equation Transcription: Text Transcription: triangle KRE angle KRL

Find \(m \angle 2\). Equation Transcription: Text Transcription: m angle 2

Find \(m \angle 5\). Equation Transcription: Text Transcription: m angle 5

Replace each with <, >, or = to make a true sentence. \(m \angle 3\) \(m \angle R L C\) Equation Transcription: Text Transcription: m angle 3 m angle RLC

Replace each with <, >, or = to make a true sentence. \(m \angle 2+m \angle 3\) \(m \angle 1\) Equation Transcription: Text Transcription: m angle 2 + m angle 3 m angle 1

In \(\triangle M P Q\), list the sides in order from least to greatest measure. Equation Transcription: Text Transcription: triangle MPQ

In \(\triangle X Y Z\), identify the angle with the greatest measure. Equation Transcription: Text Transcription: triangle XYZ

In \(\triangle B T W\), \(m \angle B=36\), \(m \angle T=84\), and \(m \angle W=60\). Which side of \(\triangle B T W\) has the greatest measure? Equation Transcription: Text Transcription: triangle BTW m angle B = 36 m angle T = 84 m angle W = 60

Is it possible for \(3,7 \text { and } 11\) to be the measures of the sides of a triangle? Explain. Equation Transcription: Text Transcription: 3, 7 and 11

In \(\triangle F G W\), \(F G=12\) and \(F W=19\). If \(G W=x\), determine the range of possible values for \(x\). Equation Transcription: Text Transcription: triangle FGW FG = 12 FW = 19 GW = x x

If \(m \angle T H M=82\), find the value of \(x\). Equation Transcription: Text Transcription: m angle THM = 82 x

The character below means mountain in Chinese. The character is enlarged on a copy machine so that it is \(3\) times as large as shown. Write a relationship comparing \(CD\) and \(EG\) in the enlarged figure using \(<\), \(>\), or \(=\). Equation Transcription: Text Transcription: 3 CD EG < > =

Jana is assembling a metal shelving unit to use in her garage. The unit uses triangular braces for support, as shown in the diagram below. Piece \(r\) is \(60\) inches long and piece \(v\) is \(25\) inches long. Find the range of possible lengths for piece \(t\) before all the pieces are permanently fastened together. Equation Transcription: Text Transcription: r 60 v 25 t

Multiple Choice In order for a student to be eligible for financial aid at a certain school, a student’s parents must have a combined annual income of less than $32,000. If f is the father’s income and m is the mother’s income, which sentence represents the condition for financial aid? 1. \(f+m<\$ 32,000\) 2. \(f+m>\$ 32,000\) 3. \(f-m<\$ 32,000\) 4. \(2 f<\$ 32,000\) Equation Transcription: 2f < $32,000 Text Transcription: $32, 000 f+m<$32,000 f+m >$32,000 f - m < $32,000 2f < $32,000

If the sum of two consecutive odd integers is \(56\), then the greater integer equals— 1. \(25\) 2. \(27\) 3. \(29\) 4. \(31\) 5. \(33\) Equation Transcription: Text Transcription: 56 25 27 29 31 33

The distance an object covers when it moves at a constant speed, or rate, is given by the formula \(d=rt\), where \(d\) is distance, \(r\) is rate, and \(t\) is time. How far does a car travel in \(2 \frac{1}{2}\) hours moving at a constant speed of \(60\) miles per hour? 1. \(30\) mi 2. \(60\) mi 3. \(150\) mi 4. \(300\) mi Equation Transcription: Text Transcription: d = rt d r t 212 60 30 150 300

If \(3\) more than \(x\) is \(2\) more than \(y\), what is \(x\) in terms of \(y\)? 1. \(y-5\) 2. \(y-1\) 3. \(y+1\) 4. \(y+5\) 5. \(y+6\) Equation Transcription: Text Transcription: 3 x 2 y y-5 y-1 y+1 y+5 y+6

The annual salaries for the eight employees in a small company are \(\$ 12,000\), \(\$ 14,500\), \(\$ 14,500\), \(\$ 18,000\), \(\$ 21,000\), \(\$ 27,000\), \(\$ 38,000\), and \(\$ 82,000\). Which of these measures of central tendency would make the company salaries seem as large as possible? 1. mean 2. median 3. mode 4. range Equation Transcription: Text Transcription: $12,000 $14,500 $18,000 $21,000 $27,000 $38,000 $82,000

Shari’s test scores in Spanish class are \(73, 86, 91\), and \(82\). She needs at least \(400\) points to earn a \(B\). Which inequality describes the number of points \(p\) Shari must yet earn in order to receive a \(B\)? 1. \(p-332>400\) 2. \(p-332>400\) 3. \(p+332 \geq 400\) 4. \(400-p \geq 332\) Equation Transcription: Text Transcription: 73, 86, 91, 82 400 B p p-332 > 400 p - 332 > 400 p + 332 400 400 - p 332

In \(\triangle A B C\), \(\angle A \cong \angle B\), and \(m \angle C\) is twice the measure of \(\angle B\). What is the measure, in degrees, of \(\angle A\)? 1. \(30\) 2. \(40\) 3. \(45\) 4. \(90\) Equation Transcription: ? Text Transcription: triangle ABC angle A congruent angle B m angle C angle B angle A 30 40 45 90

Which cannot be the perimeter of the triangle shown below? 1. \(21\) 2. \(23\) 3. \(30\) 4. \(33\) 5. \(34\) Equation Transcription: Text Transcription: 21 23 30 33 34

A car repair service charges \(\$ 36\) per hour plus the cost of the parts. If Ken is charged \(\$ 70.50\) for repairs that took \(1.5\) hours, what was the cost in dollars and cents of the parts used? Equation Transcription: Text Transcription: $36 $70.50 1.5

Mei Hua is buying a \(\$ 445\) television set that is on sale for \(30 \%\) off. The sales tax in her state is \(6 \%\). She reasons that she will save \(30 \%\), then pay \(6 \%\), so the total savings from the price listed will be \(24 \%\). She then calculates her price as \(\$ 445-0.24(\$ 445)\). Part A Calculate what answer she gets. Part B Is she right? If so, why? If not, why not, and what is the correct answer? Equation Transcription: Text Transcription: $445 30% 6% 24% $445 - 0.24($445)