# Geometry Chapter 3 & 4 Test

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1 Class: Date: Geometry Chapter 3 & 4 Test Use the diagram to find the following. 1. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4 B. angles 1 & 7, 2 & 4, and 6 & 7 D. angles 3 & 4, 7 & 8, and 1 & 6 2. Find the value of x. The diagram is not to scale. A. x = 13 B. x = 23 C. x = 40 D. none of these 1

2 3. What is the graph of y ( 2) = 1 / 3(x ( 3))? A. C. B. D. 4. Find the value of x. The diagram is not to scale. Given: SRT STR, m SRT = 34, m STU = 2x A. 17 B. 73 C. 34 D. 36 2

3 5. What is the missing reason in the two-column proof? Given: QS bisects TQR and SQ bisects TSR Prove: TQS RQS Statements Reasons 1. QS bisects TQR 1. Given 2. TQS RQS 2. Definition of angle bisector 3. QS QS 3. Reflexive property 4. SQ bisects TSR 4. Given 5. TSQ RSQ 5. Definition of angle bisector 6. TQS RQS 6.? A. AAS Theorem C. SAS Postulate B. SSS Postulate D. ASA Postulate 6. Find the values of x and y. The diagram is not to scale. A. x = 75, y = 63 C. x = 75, y = 65 B. x = 41, y = 63 D. x = 63, y = Find the value of x. The diagram is not to scale. A. 42 B. 26 C. 16 D. 64 3

4 8. What four segments are perpendicular to plane KLMJ? A. segments PQ, QR, NR, and NP C. segments MR, LQ, KP, and JN B. segments MR, LQ, NR and PQ D. segments NP, RQ, KP, and JN 9. What four segments are parallel to plane PNRQ? A. segments JN, MR, LQ, and KP C. segments JK, KL, ML, and JM B. segments KP, LQ, JK, and ML D. segments NP, RQ, PQ, and JM 10. Find the value of x. l m. The diagram is not to scale. A. 100 B. 140 C. 80 D What is the value of x? A B C D

5 12. Supply the reasons missing from the proof shown below. Given: AB AC, BAD CAD Prove: AD bisects BC Statements Reasons 1. AB AC 1. Given 2. BAD CAD 2. Given 3. AD AD 3. Reflexive Property 4. BAD CAD 4.? 5. BD CD 5.? 6. AD bisects BC 6. Definition of segment bisector A. ASA; Corresp. parts of are. C. SAS; Corresp. parts of are. B. SAS; Reflexive Property D. SSS; Reflexive Property 13. What is an equation in point-slope form for the line perpendicular to y = 4x + 7 that contains (8, 1)? A. y 1 = 4(x 8) C. y 8 = 1 (x 1) 4 B. y 1 = 1 (x 8) D. x 1 = 4(y 8) 4 5

6 14. Justify the last two steps of the proof. Given: RS UT and RT US Prove: RST UTS Proof: 1. RS UT 1. Given 2. RT US 2. Given 3. ST TS 3.? 4. RST UTS 4.? A. Reflexive Property of ; SAS C. Symmetric Property of ; SSS B. Reflexive Property of ; SSS D. Symmetric Property of ; SAS 15. Find the value of x for which p is parallel to q, if m 1 = (4x) and m 3 = 112.The diagram is not to scale. A. 108 B. 28 C. 112 D Line r is parallel to line t. Find m 6. The diagram is not to scale. A. 143 B. 33 C. 137 D. 43 6

7 17. Which two triangles are congruent by ASA? MR bisects QO, and MQP ROP. A. MNP and ONP C. MQP and MPN B. MPQ and RPO D. none 18. What common side do AEG and ADE share? A. DG C. AE B. AD D. EG 19. Find the value of x. The diagram is not to scale. Given: RS ST, m RST = 6x 60, m STU = 7x A. 150 B. 17 C. 15 D. 20 7

8 20. Two sides of an equilateral triangle have lengths 2x + 4 and 3x Which could be the length of the third side: 22 x or 6x 6? A. 22 x only C. both 22 x and 6x 6 B. 6x 6 only D. neither 22 x nor 6x What is the slope of the line shown? A. 3 5 C. 5 3 B. 5 3 D Find the values of x and y. A. x = 90, y = 42 C. x = 42, y = 48 B. x = 48, y = 42 D. x = 90, y = 48 8

9 23. What is the slope of the line shown? A. 7 9 B. 7 9 C. 9 7 D What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? A. AB AD C. CBA CDA B. BAC DAC D. AB AD 25. Find m Q. The diagram is not to scale. A. 71 B. 109 C. 81 D

10 26. Each sheet of metal on a roof is perpendicular to the top line of the roof. What can you conclude about the relationship between the sheets of roofing? Justify your answer. A. The sheets of metal are all parallel to each other by the Transitive Property of Parallel Lines. B. The sheets of metal are all parallel to each other because in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. C. The sheets of metal are all parallel to each other because in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. D. The sheets of metal are all parallel to each other by the Alternate Interior Angles Theorem. 27. The expressions in the figure below represent the measures of two angles. Find the value of x. f g. The diagram is not to scale. A. 19 B. 20 C. 21 D

11 28. What is the relationship between 3 and 5? 29. BE A. alternate interior angles C. corresponding angles B. alternate exterior angles D. same-side interior angles is the bisector of ABC and CD is the bisector of ACB. Also, XBA YCA. Which of AAS, SSS, SAS, or ASA would you use to help you prove BL CM? A. SAS B. AAS C. SSS D. ASA 30. Write the equation for the horizontal line that contains point G( 9, 6). A. x = 9 B. y = 6 C. y = 9 D. x = The folding chair has different settings that change the angles formed by its parts. Suppose m 2 is 30 and m 3 is 81. Find m 1. The diagram is not to scale. A. 121 B. 101 C. 131 D

12 32. What is an equation in slope-intercept form for the line given? A. y = 9 / 5(x) (2) C. y = 9 / 5(x) + ( 7 / 5) B. y = 5 / 9(x) + ( 7 / 5) D. y = 5 / 9(x) + ( 43 / 5) 12

13 Geometry Chapter 3 & 4 Test Answer Section 1. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: To identify angles formed by two lines and a transversal NAT: CC G.CO.1 CC G.CO.12 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-1 Problem 2 Identifying an Angle Pair KEY: corresponding angles transversal parallel lines 2. ANS: B PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle 3. ANS: B PTS: 1 DIF: L4 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: To graph and write linear equations NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 5 TOP: 3-7 Problem 2 Graphing Lines KEY: graphing slope-intercept form slope y-intercept 4. ANS: B PTS: 1 DIF: L4 REF: 3-5 Parallel Lines and Triangles OBJ: To find measures of angles of triangles NAT: CC G.CO.10 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem KEY: exterior angle of a polygon remote interior angles 5. ANS: D PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO PO 12 TOP: 4-3 Problem 2 Writing a Proof Using ASA KEY: ASA proof two-column proof 6. ANS: A PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines OBJ: To use properties of parallel lines to find angle measures NAT: CC G.CO.9 M.1.d G.3.g STA: 4.1.PO PO 12 TOP: 3-2 Problem 4 Finding an Angle Measure KEY: corresponding angles parallel lines 7. ANS: C PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles OBJ: To find measures of angles of triangles NAT: CC G.CO.10 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem KEY: triangle sum of angles of a triangle vertical angles 8. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: To identify relationships between figures in space NAT: CC G.CO.1 CC G.CO.12 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: parallel planes parallel lines 9. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: To identify relationships between figures in space NAT: CC G.CO.1 CC G.CO.12 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes KEY: parallel planes parallel lines 1

14 10. ANS: D PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines OBJ: To use properties of parallel lines to find angle measures NAT: CC G.CO.9 M.1.d G.3.g STA: 4.1.PO PO 12 TOP: 3-2 Problem 4 Finding an Angle Measure KEY: corresponding angles parallel lines angle pairs 11. ANS: D PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem Triangle Angle-Sum Theorem isosceles triangle 12. ANS: C PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 1 Using the Isosceles Triangle Theorems KEY: segment bisector isosceles triangle proof two-column proof 13. ANS: B PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: To relate slope to parallel and perpendicular lines NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 4 TOP: 3-8 Problem 4 Writing Equations of Perpendicular Lines KEY: slopes of perpendicular lines perpendicular lines 14. ANS: B PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: To prove two triangles congruent using the SSS and SAS Postulates NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO 8 TOP: 4-2 Problem 1 Using SSS KEY: SSS reflexive property proof 15. ANS: B PTS: 1 DIF: L4 REF: 3-3 Proving Lines Parallel OBJ: To determine whether two lines are parallel NAT: CC G.CO.9 G.3.b G.3.g STA: 4.1.PO PO 12 TOP: 3-3 Problem 4 Using Algebra KEY: parallel lines angle pairs 16. ANS: D PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines OBJ: To use properties of parallel lines to find angle measures NAT: CC G.CO.9 M.1.d G.3.g STA: 4.1.PO PO 12 TOP: 3-2 Problem 1 Identifying Supplementary Angles KEY: parallel lines alternate interior angles 17. ANS: B PTS: 1 DIF: L4 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: To prove two triangles congruent using the ASA Postulate and the AAS theorem NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO PO 12 TOP: 4-3 Problem 1 Using ASA KEY: ASA vertical angles 18. ANS: C PTS: 1 DIF: L3 REF: 4-7 Congruence in Overlapping Triangles OBJ: To identify congruent overlapping triangles NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO 8 TOP: 4-7 Problem 1 Identifying Common Parts KEY: overlapping triangle congruent parts 2

15 19. ANS: C PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem isosceles triangle problem solving Triangle Angle-Sum Theorem 20. ANS: A PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra KEY: equilateral triangle word problem problem solving 21. ANS: D PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: To graph and write linear equations NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 5 TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 22. ANS: A PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles and equilateral triangles NAT: CC G.CO.10 CC G.CO.13 CC G.SRT.5 G.1.c G.2.e G.3.e STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra KEY: angle bisector isosceles triangle 23. ANS: C PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: To graph and write linear equations NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 5 TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 24. ANS: D PTS: 1 DIF: L4 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: To prove two triangles congruent using the SSS and SAS Postulates NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO 8 TOP: 4-2 Problem 2 Using SAS KEY: SAS reasoning 25. ANS: A PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines OBJ: To use properties of parallel lines to find angle measures NAT: CC G.CO.9 M.1.d G.3.g STA: 4.1.PO PO 12 TOP: 3-2 Problem 3 Finding Measures of Angles KEY: angle parallel lines transversal 26. ANS: B PTS: 1 DIF: L3 REF: 3-4 Parallel and Perpendicular Lines OBJ: To relate parallel and perpendicular lines NAT: CC G.MG.3 G.3.b G.3.g STA: 4.1.PO PO 12 TOP: 3-4 Problem 1 Solving a Problem with Parallel Lines KEY: parallel perpendicular transversal word problem reasoning 27. ANS: B PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines OBJ: To use properties of parallel lines to find angle measures NAT: CC G.CO.9 M.1.d G.3.g STA: 4.1.PO PO 12 TOP: 3-2 Problem 4 Finding an Angle Measure KEY: corresponding angles parallel lines angle pairs 3

16 28. ANS: D PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: To identify angles formed by two lines and a transversal NAT: CC G.CO.1 CC G.CO.12 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-1 Problem 3 Classifying an Angle Pair KEY: angle pairs transversal parallel lines 29. ANS: D PTS: 1 DIF: L4 REF: 4-7 Congruence in Overlapping Triangles OBJ: To prove two triangles congruent using other congruent triangles NAT: CC G.SRT.5 G.2.e G.3.e G.5.e STA: 4.1.PO 8 TOP: 4-7 Problem 2 Using Common Parts KEY: corresponding parts congruent figures ASA SAS AAS SSS reasoning 30. ANS: B PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: To graph and write linear equations NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 5 TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical Lines KEY: horizontal line 31. ANS: D PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles OBJ: To find measures of angles of triangles NAT: CC G.CO.10 M.1.d G.3.g STA: 4.1.PO 4 TOP: 3-5 Problem 3 Applying the Triangle Theorems KEY: triangle sum of angles of a triangle word problem exterior angle of a polygon 32. ANS: C PTS: 1 DIF: L4 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: To graph and write linear equations NAT: CC G.GPE.5 G.3.g G.4.a G.4.d STA: 3.3.PO PO PO 5 TOP: 3-7 Problem 4 Using Two Points to Write an Equation KEY: point-slope form 4

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