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Name: ________________________ Class: ___________________ Date: __________ Geometry SIA #1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. What is the intersection of plane STXW and plane TUYX? a. ____ b. UY c. SW d. TX 2. If EF 9 and EG 26, find the value of FG. The drawing is not to scale. a. b. ____ VZ 9 17 c. d. 16 19 3. If Z is the midpoint of RT , what are x, RZ, and RT? a. b. x = 16, RZ = 42, and RT = 21 x = 18, RZ = 21, and RT = 42 c. d. 1 x = 14, RZ = 17, and RT = 34 x = 16, RZ = 21, and RT = 42 ID: A Name: ________________________ ____ ID: A 4. Complete the statement. DEF ? a. DGF b. GDF ____ c. d. DFE DFG 5. If mEOF 28 and mFOG 39, then what is the measure of EOG? The diagram is not to scale. a. 67 b. 11 c. 78 d. 56 ____ 6. MO bisects LMN, mLMO 6x 22, and mNMO 2x 30. Solve for x and find mLMN. The diagram is not to scale. a. b. x = 12, mLMN 100 x = 13, mLMN 56 c. d. 2 x = 12, mLMN 50 x = 13, mLMN 112 Name: ________________________ ____ ID: A 7. Find the values of x and y. c. d. x = 36, y = 144 x = 20, y = 9 8. Identify a pair of same-side interior angles. a. 1 and 7 b. 2 and 5 c. d. 8 and 7 3 and 8 9. What are three pairs of corresponding angles? a. angles 1 & 8, 2 & 3, and 4 & 5 b. angles 1 & 7, 8 & 6, and 3 & 5 c. d. angles 1 & 2, 5 & 6, and 4 & 7 angles 1 & 2, 3 & 8, and 4 & 7 a. b. x = 144, y = 36 x = 9, y = 20 Use the diagram to find the following. ____ ____ 3 Name: ________________________ ID: A ____ 10. Line f is parallel to line g. Find the value of x. The diagram is not to scale. a. –14 b. 15 c. 13 d. 14 ____ 11. Which lines are parallel if m4 m7? Justify your answer. a. b. c. d. l l r r m, by the Converse of the Same-Side Interior Angles Theorem m, by the Converse of the Alternate Interior Angles Theorem s, by the Converse of the Alternate Interior Angles Theorem s, by the Converse of the Same-Side Interior Angles Theorem ____ 12. Find the value of x for which p is parallel to q, if m1 3x and m3 102.The diagram is not to scale. a. 99 b. 102 c. 4 34 d. 105 Name: ________________________ ID: A ____ 13. Find the value of x for which l is parallel to m. The diagram is not to scale. a. 160 b. 80 c. 141 d. 39 c. 145 d. 97 c. 28 d. 43 M d. none of these ____ 14. Find the value of x. The diagram is not to scale. a. 42 b. 83 ____ 15. Find the value of x. The diagram is not to scale. a. 18 b. 65 ____ 16. Name the angle included by the sides PN and NM . a. N b. P c. 5 Name: ________________________ ID: A ____ 17. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? a. b. AC BD CBA CDA c. d. BAC DAC AC BD c. d. VTU and ABC ABC and TUV ____ 18. Which triangles are congruent by ASA? a. b. none VTU and HGF 6 Name: ________________________ ID: A ____ 19. 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 2. TQS RQS 3. QS QS 1. Given 2. Definition of angle bisector 3. Reflexive property 4. SQ bisects TSR 5. TSQ RSQ 6. TQS RQS a. b. 4. Given 5. Definition of angle bisector 6. ? SAS Postulate ASA Postulate c. d. SSS Postulate AAS Theorem c. 66° ____ 20. What is the value of x? a. 71° b. 142° 7 d. 132° ID: A Geometry SIA #1 Answer Section MULTIPLE CHOICE 1. ANS: OBJ: TOP: DOK: 2. ANS: OBJ: TOP: DOK: 3. ANS: OBJ: TOP: DOK: 4. ANS: OBJ: TOP: DOK: 5. ANS: OBJ: TOP: DOK: 6. ANS: OBJ: STA: TOP: KEY: 7. ANS: OBJ: STA: TOP: KEY: DOK: 8. ANS: OBJ: STA: KEY: 9. ANS: OBJ: STA: KEY: D PTS: 1 DIF: L3 REF: 1-2 Points, Lines, and Planes 1-2.1 Understand basic terms and postulates of geometry STA: MA.912.G.8.1 1-2 Problem 3 Finding the Intersection of Two Planes KEY: plane | intersection of two planes DOK 2 B PTS: 1 DIF: L2 REF: 1-3 Measuring Segments 1-3.1 Find and compare lengths of segments STA: MA.912.G.1.1 1-3 Problem 2 Using the Segment Addition Postulate KEY: segment | segment length DOK 1 D PTS: 1 DIF: L3 REF: 1-3 Measuring Segments 1-3.1 Find and compare lengths of segments STA: MA.912.G.1.1 1-3 Problem 4 Using the Midpoint KEY: segment | segment length | midpoint DOK 2 A PTS: 1 DIF: L3 REF: 1-4 Measuring Angles 1-4.1 Find and compare the measures of angles 1-4 Problem 3 Using Congruent Angles KEY: congruent angles DOK 2 A PTS: 1 DIF: L3 REF: 1-4 Measuring Angles 1-4.1 Find and compare the measures of angles 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition Postulate DOK 2 D PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs 1-5.1 Identify special angle pairs and use their relationships to find angle measures MA.912.G.4.2 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures angle bisector DOK: DOK 2 D PTS: 1 DIF: L4 REF: 2-6 Proving Angles Congruent 2-6.1 Prove and apply theorems about angles MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5 2-6 Problem 1 Using the Vertical Angles Theorem Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question DOK 2 C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles 3-1.2 Identify angles formed by two lines and a transversal MA.912.G.7.2 TOP: 3-1 Problem 2 Identifying an Angle Pair transversal | angle pair DOK: DOK 1 B PTS: 1 DIF: L3 REF: 3-1 Lines and Angles 3-1.2 Identify angles formed by two lines and a transversal MA.912.G.7.2 TOP: 3-1 Problem 2 Identifying an Angle Pair angle pair | transversal DOK: DOK 1 1 ID: A 10. ANS: OBJ: STA: KEY: 11. ANS: OBJ: TOP: DOK: 12. ANS: OBJ: TOP: DOK: 13. ANS: OBJ: TOP: DOK: 14. ANS: OBJ: STA: TOP: KEY: 15. ANS: OBJ: STA: TOP: KEY: 16. ANS: REF: OBJ: STA: KEY: 17. ANS: REF: OBJ: STA: KEY: 18. ANS: REF: OBJ: STA: KEY: 19. ANS: REF: OBJ: STA: TOP: DOK: D PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines 3-2.2 Use properties of parallel lines to find angle measures MA.912.G.1.3 TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure corresponding angles | parallel lines | angle pairs DOK: DOK 2 B PTS: 1 DIF: L2 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 1 Identifying Parallel Lines KEY: parallel lines | reasoning DOK 2 C PTS: 1 DIF: L4 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 4 Using Algebra KEY: parallel lines | angle pairs DOK 2 B PTS: 1 DIF: L3 REF: 3-3 Proving Lines Parallel 3-3.1 Determine whether two lines are parallel STA: MA.912.G.1.3| MA.912.G.8.5 3-3 Problem 4 Using Algebra KEY: parallel lines | transversal DOK 2 B PTS: 1 DIF: L2 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 2 Using the Triangle Exterior Angle Theorem triangle | sum of angles of a triangle DOK: DOK 2 A PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles 3-5.2 Find measures of angles of triangles MA.912.G.2.2| MA.912.G.4.1| MA.912.G.8.5 3-5 Problem 2 Using the Triangle Exterior Angle Theorem triangle | sum of angles of a triangle | vertical angles DOK: DOK 2 A PTS: 1 DIF: L2 4-2 Triangle Congruence by SSS and SAS 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS angle DOK: DOK 1 A PTS: 1 DIF: L4 4-2 Triangle Congruence by SSS and SAS 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS SAS | reasoning DOK: DOK 2 C PTS: 1 DIF: L2 4-3 Triangle Congruence by ASA and AAS 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA ASA DOK: DOK 1 B PTS: 1 DIF: L3 4-3 Triangle Congruence by ASA and AAS 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 4-3 Problem 2 Writing a Proof Using ASA KEY: ASA | proof DOK 2 2 ID: A 20. ANS: REF: OBJ: STA: KEY: DOK: C PTS: 1 DIF: L2 4-5 Isosceles and Equilateral Triangles 4-5.1 Use and apply properties of isosceles and equilateral triangles MA.912.G.4.1 TOP: 4-5 Problem 2 Using Algebra isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem DOK 2 3