Geometry

User: Aariella Albury E-Mail: [email protected] In Course: GEO ( 4498) Instructor: Kelly Dale

Exam: 05.05 Module Five Review and Practice Exam

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Question 1 (Multiple Choice Worth 1 points) (05.01 LC)

Look at the figure shown below:

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Rita is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 24.

Statement Reason

1. Segment ST is parallel to segment QR

Given

2. Angle QRT is congruent to angle STP

Corresponding angles formed by parallel lines and their transversal are congruent

3. Angle SPT is congruent to angle QPR

Reflexive property of angles

4. Triangle SPT is congruent to triangle QPR

Angle-Angle Similarity Postulate

5. (2x + 28):95 = Corresponding sides of similar triangles are in proportion

Which of the following can she use to complete statement 5?

28:95

28:35

60:95

60:35

Question 2 (Multiple Choice Worth 1 points) (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 below:

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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?

4:9 ≠ 6:13

4:9 ≠ 6:7

4:13 ≠ 6:9

4:5 ≠ 6:13

Question 3 (Multiple Choice Worth 1 points) (05.03 MC)

Look at the figure below:

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

Triangle ACD and triangle ACE

Triangle AEC and triangle DEC

Triangle ABE and triangle ACE

Triangle AEB and triangle DEC

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Question 4 (Multiple Choice Worth 1 points) (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.

If the length of AO is double the length of CO, the length of DC is

half of the length of AB

one-fourth the length of DB

double the length of AO

equal to the length of OB

Question 5 (Multiple Choice Worth 1 points) (05.03 LC)

The figure below shows segments KL and MN which intersect at point P. Segment KM is parallel to segment LN.

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Previous Question Next QuestionQuestion 1 (Not Answered) 0

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Which of these facts is used to prove that triangle KMP is similar to triangle LNP?

Angle KMP is congruent to angle LPN.

Angle KMP is congruent to angle LNP.

Angle KPM is congruent to angle PLN.

Angle KPM is congruent to angle LNP.

Question 6 (Multiple Choice Worth 1 points) (05.01 LC)

Look at the right triangle ABC:

A student made the following chart to prove that AB + BC = AC :

Statement Justification

1. Triangle ABC is similar to triangle BDC

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

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

5. AB + BC = AC • AD + AC • DC = AC (AD + DC)

5. Adding Statement 1 and Statement 2

6. AB + BC = AC 6. AD + DC = AC

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2 2 2

2

2

2 2

2 2 2

Which justification is incorrect?

Justification 4

Justification 1

Justification 2

Justification 3

Question 7 (Multiple Choice Worth 1 points) (05.01 LC)

The figure below shows two triangles EFG and KLM:

Which of the following can be used to prove that triangle EFG is also a right triangle?

Prove that a + b is greater than c in triangle EFG so c = a + b .

Prove that the sum of the squares of a and c in triangle EFG is greater than square of b in triangle KLM.

Prove that KL = EF so in triangle KLM a + b = c .

Prove that KL = EF so in triangle KLM c = a + b , which makes triangle EFG a right triangle.

Question 8 (Multiple Choice Worth 1 points)

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2 2 2

2 2 2

2 2 2

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(05.01 MC)

The figure shows three right triangles. Triangles PQS, QRS, and PRQ are similar.

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

Using the given theorem, which two statements help to prove that if segment PR is x, then x = 97?

Segment PR • segment PS = 16 Segment PR • segment SR = 36

Segment PR • segment PS = 36 Segment PR • segment SR = 81

Segment PR • segment PS = 16 Segment PR • segment SR = 81

Segment PR • segment PS = 81 Segment PR • segment SR = 16

Question 9 (Multiple Choice Worth 1 points) (05.03 MC)

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

2

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Jake 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

  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

SAS postulate

Which of the following completes Jake's proof?

In triangles APD and BPC; AD = BC

In triangles APD and BPC; AP = PB

In triangles APB and DPC; AD = BC

In triangles APB and DPC; AP = PB

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