# Which step can be used to prove that triangle

Question

05.00 Module Five Pretest

Question 1(1 point)

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(05.01 MC)

The figure below shows two triangles EFG and KLM:

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Which step can be used to prove that triangle EFG is also a right triangle? (1 points)

Question 1 options:

1)

Prove that the sum of a and c is greater than b.

2)

Prove that the sum of a and b is greater than c.

3)

Prove that triangles are congruent by SSS property and hence, angle EGF is equal to angle KML.

4)

Prove that the ratio of EF and KL is greater than 1 and hence, the triangles are similar by AA postulate.

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Question 2(1 point)

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(05.01 HC)

Look at the right triangle ABC:

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A student made the following chart to prove that AB2 + BC2 = AC2:

Statement

Justification

1. Triangle ABC is similar to triangle BDC

1. Angle ABC = Angle BDC and Angle BCA = Angle BCD

2. BC2 = AC x DC

2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC

3. Triangle ABC is similar to triangle ABD

3. Angle ABC = Angle BAD and Angle BAC = Angle ABD

4. AB2 = AC x AD

4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB

5. AB2+ BC2= AC x AD + AC x DC = AC (AD + DC)

5. Adding Statement 1 and Statement 2

6. AB2+ BC2= AC2

6. AD + DC = AC

What is the flaw in the student’s proof? (1 points)

Question 2 options:

1)

Justification 4 should be “AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD.”

2)

Justification 1 should be “Angle ABC = Angle BCD and Angle BCA = Angle DBC.”

3)

Justification 2 should be “BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC.”

4)

Justification 3 should be “Angle ABC = Angle ADB and Angle BAC = Angle BAD.”

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Question 3(1 point)

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(05.01 MC)

Look at the figure shown below:

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Nora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 45.

Statement

Reason

1.

Segment ST is parallel to segment RQ

Given

2.

Angle QRS is congruent to angle TSP

Corresponding angles formed by parallel lines and their transversal are congruent.

3.

Angle SPT is congruent to angle RPQ

Reflexive property of angles.

4.

Triangle SPT is similar to triangle RPQ

Angle-Angle Similarity Postulate

5.

?

Corresponding sides of similar triangles are in proportion.

Which equation can she use as statement 5? (1 points)

Question 3 options:

1)

60:x = 48:(48 + 36)

2)

60 + x = 48 + 36

3)

60 – x = 48 – 36

4)

60:(60+x) = 48:(48 + 36)

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Question 4(1 point)

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(05.01 MC)

Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown:

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She starts with the assumption that segment DE is parallel to segment BC.

Which inequality will she use to contradict the assumption? (1 points)

Question 4 options:

1)

4:9 ≠ 6:13

2)

4:9 ≠ 6:7

3)

4:13 ≠ 6:9

4)

4:5 ≠ 6:13

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Question 5(1 point)

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(05.01 HC)

The figure shows three right triangles. Triangles JKM, KLM, and JLK are similar.

Theorem: If two triangles are similar, the corresponding sides are in proportion.

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Using the given theorem, which two statements help to prove that if segment JL is x, then x2 = 100? (1 points)

Question 5 options:

1)

Segment JL x segment JM = 64

Segment JL x segment LM = 48

2)

Segment JL x segment JM = 48

Segment JL x segment LM = 36

3)

Segment JL x segment JM = 64

Segment JL x segment LM = 36

4)

Segment JL x segment JM = 36

Segment JL x segment LM = 64

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Question 6(1 point)

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(05.03 MC)

The figure below shows segments AC and EF which intersect at point B. Segment AF is parallel to segment EC.

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Which of these facts is used to prove that triangle ABF is similar to triangle CBE? (1 points)

Question 6 options:

1)

Angle AFB is congruent to angle CEB because corresponding angles are congruent.

2)

Angle ABF is congruent to angle CBE because vertical angles are congruent.

3)

Line segment AF is congruent to line segment EC because parallel segments are congruent.

4)

Line segment AB is congruent to line segment FB because legs of an isosceles triangle are congruent.

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Question 7(1 point)

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(05.03 MC)

Look at the figure:

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Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? (1 points)

Question 7 options:

1)

Triangle ACD and triangle ACE

2)

Triangle AEC and triangle DEC

3)

Triangle ABE and triangle ACE

4)

Triangle AEB and triangle DEC

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Question 8(1 point)

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(05.03 HC)

The figure below shows a square ABCD and an equilateral triangle DPC:

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Jim makes the chart shown below to prove that triangle APD is congruent to triangle BPC:

Statements

Justifications

In triangles APD and BPC; DP = PC

Sides of equilateral triangle DPC are equal

In triangles APD and BPC; AD = BC

Sides of square ABCD are equal

In triangles APD and BPC; angle ADP = angle BCP

Angle ADC = angle BCD = 90° and angle ADP = angle BCP = 90° – 60° = 30°

Triangles APD and BPC are congruent

SSS postulate

What is the error in Jim’s proof? (1 points)

Question 8 options:

1)

He writes DP = PC instead of DP = PB.

2)

He writes AD = BC instead of AD = PC.

3)

He assumes the measure of angle ADP and angle BCP as 30° instead of 45°.

4)

He assumes that the triangles are congruent by the SSS postulate instead of SAS postulate.

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Question 9(1 point)

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(05.03 HC)

The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O.

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If the length of AO is three times the length of CO, the length of BO is (1 points)

Question 9 options:

1)

one-third the length of AC

2)

one-third the length of AB

3)

three times the length of DO

4)

three times the length of DC

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Question 10(1 point)

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(05.01 HC)

Use ΔABC and ΔEDF shown below to answer the question that follows:

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If∠B≅∠D and∠A≅∠E, prove that .0/msohtmlclip1/01/clip_image012.gif” alt=”Description: https://njvs.desire2learn.com/content/enforced/14032-4346/0500modulefivepretest/0500_g10_q2.gif?_&d2lsessionval=” qo2n6tgflktnsnjxjelfdamaf””=””>. (1 points)

Question 10 options:

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08.09 Module Eight Exam Part One

Question 1(5 points)

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(08.01 MC)

Find the volume of a cylinder with a height of 2 meters and a diameter that is 5 times the measure of the height. Use 3.14 for pi, and round your answer to the nearest hundredth. (5 points)

Question 1 options:

1)

157 m3

2)

339.12 m3

3)

678.24 m3

4)

1570 m3

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Question 2(5 points)

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(08.01 MC)

Find the volume of a cone with a diameter of 9 inches and a height that is 5 times the radius. Use 3.14 for pi, and round your answer to the nearest hundredth. (5 points)

Question 2 options:

1)

47.1 in3

2)

78.51in3

3)

476.89 in3

4)

1430.66 in3

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Question 3(5 points)

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(08.01 MC)

Find the length of the base of a square pyramid if the volume is 48 cubic inches and has a height of 9 inches. (5 points)

Question 3 options:

1)

4 inches

2)

8 inches

3)

16 inches

4)

24 inches

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Question 4(5 points)

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(08.02 MC)

A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 2 inches. The vase is filled with water up to a height of 8 inches.

What is the volume of water in the vase? (5 points)

Question 4 options:

1)

26π in3

2)

16π in3

3)

24π in3

4)

32π in3

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Question 5(5 points)

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(08.02 MC)

A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:

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What is the total volume of grains that can be stored in the silo? (5 points)

Question 5 options:

1)

14π ft3

2)

30π ft3

3)

24π ft3

4)

18π ft3

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Question 6(5 points)

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(08.02 MC)

A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inches thick:

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What is the approximate inside volume of the pipe? (5 points)

Question 6 options:

1)

332 cubic inches

2)

69 cubic inches

3)

703 cubic inches

4)

99 cubic inches

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Question 7(5 points)

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(08.04 MC)

A piece of aluminum occupies a volume of 13.0 milliliters and weighs 52.9 grams. What is its density of the aluminum rounded to the nearest hundredth? Only enter numerical values, which can include a decimal point. (5 points)

Question 7 options:

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Question 8(5 points)

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(08.04 MC)

What is the weight (in grams) of a liquid that exactly fills a 465.0 milliliter container if the density of the liquid is 0.982 .0/msohtmlclip1/01/clip_image015.gif” alt=”Description: https://njvs.desire2learn.com/content/enforced/14032-4346/0809moduleeightexampartone/0809_g8.gif?_&d2lsessionval=” qo2n6tgflktnsnjxjelfdamaf””=””>? Round to the nearest hundredth when necessary and only enter numerical values, which can include a decimal point. (5 points)

Question 8 options:

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Question 9(5 points)

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(08.04 MC)

A large emerald with a mass of 982.7 grams was recently discovered in a mine. If the density of the emerald is 2.76 .0/msohtmlclip1/01/clip_image016.png” alt=”Description: https://njvs.desire2learn.com/content/enforced/14032-4346/0809moduleeightexampartone/0809_g33.png?_&d2lsessionval=” qo2n6tgflktnsnjxjelfdamaf””=””>, what is the volume? Round to the nearest hundredth when necessary and only enter numerical values, which can include a decimal point. (5 points)

Question 9 options:

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Question 10(5 points)

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(08.05 MC)

If a rectangle was rotated about the y-axis, like the one shown below, what would be the resulting three-dimensional shape?

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Question 10 options:

1)

Cone

2)

Cylinder

3)

Pyramid

4)

Sphere

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