Geometry Module 3 Unit 2 Practice Exam
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1 Name: Class: Date: Geometry Module 3 Unit 2 Practice Exam Short Answer 1. If BCDE is congruent to OPQR, then BC is congruent to?. 2. NPM? 3. Given QRS TUV, QS 4v 3, and TV 8v 9, find the length of QS and TV. 4. Given ABC PQR, m B 3v 1, and m Q 8v 9, find m B and m Q. 5. In the paper airplane, ABCD EFGH, m B m BCD 90, and m BAD 132. Find m GHE. 1
2 Name: 6. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to scale. 7. Use the information given in the diagram. Tell why UX VW and VWU XUW. 8. If m B m D 30, find m C so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. 2
3 Name: 9. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. 10. If ON 8x 8, LM 7x 5, NM x 5, and OL 5y 4, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. 11. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. 3
4 Name: 12. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY NW 13. What is the most precise name for quadrilateral ABCD with vertices A( 3, 3), B( 3, 1), C(2, 1), and D(2, 3)? 14. In the rhombus, m 1 30x, m 2 x y, and m 3 3z. Find the value of each variable. The diagram is not to scale. 15. In the rhombus, m What are m 2 and m 3? The diagram is not to scale. 4
5 Name: 16. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. 17. DEFG is a rectangle. DF = 4x 5 and EG = x + 7. Find the value of x and the length of each diagonal. 18. In rectangle KLMN, KM = 10x 15 and LN = 45. Find the value of x. 19. In rectangle PQRS, PR = 20x 14 and QS = x Find the value of x and the length of each diagonal. 20. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. 5
6 Name: 21. In quadrilateral ABCD, m ACD 2x 4 and m ACB 5x 2. For what value of x is ABCD a rhombus? 22. In quadrilateral ABCD, AE x 22 and BE 3x 18. For what value of x is ABCD a rectangle? 23. Find the values of a and b.the diagram is not to scale. 24. In quadrilateral MNOP, M N. Which of a parallelogram, trapezoid, or rhombus could quadrilateral MNOP be? 25. J and M are base angles of isosceles trapezoid JKLM. If m J 17x 6, and m M 10x 13, find m K. 6
7 Name: 26. The isosceles trapezoid is part of an isosceles triangle with a 58 vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale. 27. LM is the midsegment of ABCD. AB 27 and DC 167. What is LM? 28. LM is the midsegment of ABCD. AB x 8, LM 4x 3, and DC 320. What is the value of x? 7
8 Name: 29. Find m 1 and m 3 in the kite. The diagram is not to scale. 30. m R 150 and m S 90. Find m T. The diagram is not to scale. 31. Find the values of the variables and the lengths of the sides of this kite. 8
9 Geometry Module 3 Unit 2 Practice Exam Answer Section SHORT ANSWER 1. ANS: OP PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 1 Finding Congruent Parts KEY: congruent figures corresponding parts word problem 2. ANS: BCA PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 1 Finding Congruent Parts KEY: congruent figures corresponding parts DOK: DOK 1 3. ANS: 15 PTS: 1 DIF: L4 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent figures corresponding parts 4. ANS: 7 PTS: 1 DIF: L4 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent figures corresponding parts 5. ANS: 48 PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent figures corresponding parts 1
10 6. ANS: 40 PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent figures corresponding parts 7. ANS: Given, Given PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts STA: MA.912.G.2.3 MA.912.G.2.4 MA.912.G.4.6 TOP: 4-1 Problem 4 Proving Triangles Congruent KEY: congruent figures corresponding parts proof 8. ANS: 150 PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: Determine whether a quadrilateral is a parallelogram TOP: 6-3 Problem 1 Finding Values for Parallelograms 9. ANS: x = 7, y = 5 KEY: opposite angles parallelogram PTS: 1 DIF: L3 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: Determine whether a quadrilateral is a parallelogram TOP: 6-3 Problem 1 Finding Values for Parallelograms 10. ANS: x = 13, y = 12 5 KEY: algebra parallelogram diagonal PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: Determine whether a quadrilateral is a parallelogram TOP: 6-3 Problem 1 Finding Values for Parallelograms KEY: algebra parallelogram opposite sides 2
11 11. ANS: Yes; opposite angles are congruent. PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: Determine whether a quadrilateral is a parallelogram TOP: 6-3 Problem 2 Deciding Whether a Quadrilateral Is a Parallelogram KEY: opposite angles parallelogram 12. ANS: Yes; diagonals of a parallelogram bisect each other. PTS: 1 DIF: L2 REF: 6-3 Proving That a Quadrilateral Is a Parallelogram OBJ: Determine whether a quadrilateral is a parallelogram TOP: 6-3 Problem 2 Deciding Whether a Quadrilateral Is a Parallelogram KEY: parallelogram opposite sides 13. ANS: rectangle PTS: 1 DIF: L4 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Define and classify special types of parallelograms TOP: 6-4 Problem 1 Classifying Special Parallelograms KEY: parallelogram quadrilateral special quadrilaterals rectangle square DOK: DOK ANS: x = 3, y = 87, z = 30 PTS: 1 DIF: L4 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 2 Finding Angle Measures KEY: algebra diagonal rhombus 15. ANS: m 2 = 108, m 3 36 PTS: 1 DIF: L3 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 2 Finding Angle Measures KEY: diagonal rhombus 3
12 16. ANS: m 1 90, m 2 = 35, and m 3 55 PTS: 1 DIF: L3 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 2 Finding Angle Measures KEY: diagonal rhombus 17. ANS: x = 4, DF = 11, EG = 11 PTS: 1 DIF: L3 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 3 Finding Diagonal Length 18. ANS: 3 4 KEY: rectangle algebra diagonal PTS: 1 DIF: L2 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 3 Finding Diagonal Length KEY: rectangle algebra diagonal 19. ANS: x = 28, PR = 546, QS = 546 PTS: 1 DIF: L3 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Use properties of diagonals of rhombuses and rectangles TOP: 6-4 Problem 3 Finding Diagonal Length KEY: rectangle algebra diagonal 20. ANS: Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. PTS: 1 DIF: L3 REF: 6-5 Conditions for Rhombuses, Rectangles, and Squares OBJ: Determine whether a parallelogram is a rhombus or rectangle TOP: 6-5 Problem 1 Identifying Special Parallelograms 21. ANS: 2 KEY: rectangle algebra diagonal PTS: 1 DIF: L3 REF: 6-5 Conditions for Rhombuses, Rectangles, and Squares OBJ: Determine whether a parallelogram is a rhombus or rectangle TOP: 6-5 Problem 2 Using Properties of Special Parallelograms KEY: parallelogram rhombus reasoning
13 22. ANS: 20 PTS: 1 DIF: L3 REF: 6-5 Conditions for Rhombuses, Rectangles, and Squares OBJ: Determine whether a parallelogram is a rhombus or rectangle TOP: 6-5 Problem 2 Using Properties of Special Parallelograms KEY: parallelogram rhombus reasoning 23. ANS: a 136, b 57 PTS: 1 DIF: L2 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 1 Finding Angle Measures in Trapezoids 24. ANS: any of the three PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 1 Finding Angle Measures in Trapezoids KEY: quadrilateral rectangle rhombus trapezoid parallelogram reasoning 25. ANS: 157 KEY: trapezoid base angles PTS: 1 DIF: L4 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 2 Finding Angle Measures in Isosceles Trapezoids KEY: algebra isosceles trapezoid base angles trapezoid 26. ANS: 61 ; 119 PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 2 Finding Angle Measures in Isosceles Trapezoids KEY: trapezoid isosceles trapezoid base angles isosceles triangle 5
14 27. ANS: 97 PTS: 1 DIF: L2 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 3 Using the Midsegment of a Trapezoid 28. ANS: 46 PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 3 Using the Midsegment of a Trapezoid 29. ANS: 38, 52 PTS: 1 DIF: L3 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 4 Finding Angle Measures in Kites 30. ANS: 30 PTS: 1 DIF: L2 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 4 Finding Angle Measures in Kites 31. ANS: x = 5, y = 10; 7, 13 KEY: trapezoid base angles KEY: trapezoid base angles KEY: kite diagonal KEY: kite sum of interior angles PTS: 1 DIF: L4 REF: 6-6 Trapezoids and Kites TOP: 6-6 Problem 4 Finding Angle Measures in Kites KEY: algebra kite 6
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