Geometry Chapter 3 Final Review

Geometry Chapter 3 Final Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Find the value of k. The diagram is not to scale.

a. 28 b. 94 c. 123 d. 86

____ 2. Find the values of x, y, and z. The diagram is not to scale.

a. x  66, y  96, z  84 c. x  66, y  84, z  96 b. x  84, y  96, z  66 d. x  84, y  66, z  96 ____ 3. Classify the triangle by its sides. The diagram is not to scale.

a. equilateral b. scalene c. straight d. isosceles

____ 4. Classify ABC by its angles, when mA = 39, mB = 84, and mC = 57.

a. obtuse b. straight c. right d. acute

____ 5. Find the value of the variable. The diagram is not to scale.

a. 44 b. 66 c. 20 d. 30

____ 6. Write an equation in point-slope form of the line through point J(–5, –7) with slope 2.

a. y  7  2 x  5 ( ) c. y  7  2 x  5 ( ) b. y  7  2 x  5 ( ) d. y  7  2 x  5 ( )

____ 7. Write an equation in point-slope form, y – y

= m(x – x

), of the line through points (8, –9) and (1, 5) Use (8, –9) as the point (x

, y

).

a. (y – 9) = 2(x + 8) c. (y + 9) = –2(x – 8)

b. (y – 9) = –2(x + 8) d. (y + 9) = 2(x – 8) ____ 8. Write an equation for the horizontal line that contains point E(4, 7).

a. y = 4 b. y = 7 c. x = 7 d. x = 4

____ 9. Write an equation in slope-intercept form of the line through points S(–7, –7) and T(8, 2).

a. y  3 5 x + 14

5 c. y  3

5 x – 14 5 b. y = 3

5 x + 14

5 d. y = 3

5 x – 14 5

____ 10. Is the line through points P(–3, 0) and Q(5, 6) parallel to the line through points R(–4, –5) and S(2, –1)?

Explain.

a. No, the lines have unequal slopes.

b. No, one line has slope, the other has no slope.

c. Yes; the lines have equal slopes.

d. Yes; the lines are both vertical.

____ 11. Write an equation for the line parallel to y = –8x – 2 that contains P(–6, 9).

a. y + 9 = –8(x + 6) c. x – 9 = 8(y + 6)

b. y – 9 = –8(x + 6) d. y – 9 = 8(x + 6)

____ 12. Write an equation for the line perpendicular to y = –4x + 7 that contains (–3, 3).

a. y – 3 = 1

4 (x + 3) c. y – 3 = –4(x + 3)

b. y – 3 = - 1

4 (x + 3) d. x – 3 = –4(y + 3)

____ 13. Are the lines y = –x – 8 and 5x – 5y = 25 perpendicular? Explain.

a. No; their slopes are not opposite reciprocals.

b. No; their slopes are not equal c. Yes; their slopes have product –1.

d. Yes; their slopes are equal.

____ 14. Graph 3x  5y  15.

a. c.

b. d.

____ 15. Which angles are corresponding angles?

a. 8 and 3 c. 3 and 11

b. 7 and 3 d. none of these

____ 16. Which statement is true?

a. CBE and DEB are same-side interior angles.

b. FEG and DEB are same-side interior angles.

c. FEG and CBE are alternate angles.

d. CBE and DEB are alternate angles.

____ 17. Line r is parallel to line t. Find m5. The diagram is not to scale.

a. 38 b. 132 c. 148 d. 48

____ 18. Find the value of the variable if m Ä l, m1 = 2x  30 and m5 = 4x  16. The diagram is not to scale.

a. 6 b. –7 c. 7 d. 8

____ 19. Complete the statement. If a transversal intersects two parallel lines, then ____.

a. corresponding angles are supplementary b. same-side interior angles are complementary c. alternate interior angles are congruent d. none of these

____ 20. Complete the statement. If a transversal intersects two parallel lines, then ____ angles are supplementary.

a. acute c. alternate interior

b. corresponding d. same-side interior

____ 21. Which lines, if any, can you conclude are parallel given that m1  m2  180? Justify your conclusion with a theorem or postulate.

a. g Ä h, by the Converse of the Alternate Interior Angles Theorem

b. j Ä k , by the Converse of the Same-Side Interior Angles Theorem

c. j Ä k , by the Converse of the Alternate Interior Angles Theorem

d. g Ä h, by the Converse of the Same-Side Interior Angles Theorem

____ 22. m1  4x and m3  120. Find the value of x for p to be parallel to q. The diagram is not to scale.

a. 124 b. 120 c. 30 d. 116

____ 23. Find the value of x. The diagram is not to scale.

a. 162 b. 147 c. 33 d. 75

____ 24. Find the value of x. The diagram is not to scale.

Given: SRT  STR, mSRT  73, mSTU  2x

a. 74 b. 53 c. 32 d. 106

____ 25. What must be true about the slopes of two perpendicular lines, neither of which is vertical?

a. The slopes have product –1.

b. The slopes have product 1.

c. One of the slopes must be 0.

d. The slopes are equal.

____ 26. Find the values of x and y. The diagram is not to scale.

a. x = 77, y = 59 c. x = 41, y = 57

b. x = 57, y = 77 d. x = 77, y = 57

____ 27. Find mQ. The diagram is not to scale.

a. 120 b. 60 c. 110 d. 70

____ 28. The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 26 and m3 is 70. Find m1. The diagram is not to scale.

a. 106 b. 116 c. 96 d. 86

____ 29. Graph y = 1 5 x + 3.

a. c.

b.

____ 30. Graph the line that goes through point (–5, 5) with slope 1 5 .

a. c.

b. d.

____ 31. Write an equation in slope-intercept form of the line through point P(–10, 1) with slope –5.

a. y – 1 = –5(x + 10) c. y = –5x – 49

b. y = –5x + 1 d. y – 10 = –5(x + 1)

____ 32. Which two lines are parallel?

I. 5y  3x  5 II. 5y  1  3x III. 3y  2x  1

a. II and III c. I and III

b. I and II d. No two of the lines are parallel.

____ 33. Is the line through points P(0, –9) and Q(2, –8) perpendicular to the line through points R(1, 4) and S(3, 3)?

Explain.

a. Yes; their slopes have product –1 b. No; thier slopes are not equal.

c. Yes; their slopes are equal.

d. No; their slopes are not reciprocals.

____ 34. Give the slope-intercept form of the equation of the line that is perpendicular to 7x + 3y = 18 and contains P(6, 8).

a. y – 6 = 3

7 (x – 8) c. y – 8 = 3

7 (x – 6) b. y = 3

7 x  18

7 d. y = 3

7 x + 38 7

Short Answer

35. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.

Given: l Ä n Prove: 4  6

Statments Reasons 1. l Ä n

2. 2  6 3. 4  2 4. 6  4

1. Given

a. ?

b. ?

c. ?

36. State the missing reasons in this proof.

Given: 1  5 Prove: p Ä r

Statements Reasons 1. 1  5

2. 4  1 3. 4  5 4. p Ä r

Given a.____

b.____

c.____

Geometry Chapter 3 Final Review Answer Section

MULTIPLE CHOICE

1. ANS: B OBJ: 3-4.1 Finding Angle Measures in Triangles 2. ANS: D OBJ: 3-4.1 Finding Angle Measures in Triangles 3. ANS: B OBJ: 3-4.1 Finding Angle Measures in Triangles 4. ANS: D OBJ: 3-4.1 Finding Angle Measures in Triangles 5. ANS: C OBJ: 3-4.1 Finding Angle Measures in Triangles 6. ANS: C OBJ: 3-6.2 Writing Equations of Lines

7. ANS: C OBJ: 3-6.2 Writing Equations of Lines 8. ANS: B OBJ: 3-6.2 Writing Equations of Lines 9. ANS: D OBJ: 3-6.2 Writing Equations of Lines 10. ANS: A OBJ: 3-7.1 Slope and Parallel Lines 11. ANS: B OBJ: 3-7.1 Slope and Parallel Lines

12. ANS: A OBJ: 3-7.2 Slope and Perpendicular Lines 13. ANS: C OBJ: 3-7.2 Slope and Perpendicular Lines 14. ANS: A OBJ: 3-6.1 Graphing Lines

15. ANS: C OBJ: 3-1.1 Identifying Angles 16. ANS: A OBJ: 3-1.1 Identifying Angles

17. ANS: B OBJ: 3-1.2 Properties of Parallel Lines 18. ANS: C OBJ: 3-1.2 Properties of Parallel Lines 19. ANS: C OBJ: 3-1.2 Properties of Parallel Lines 20. ANS: D OBJ: 3-1.2 Properties of Parallel Lines 21. ANS: B OBJ: 3-2.1 Using a Transversal

22. ANS: C OBJ: 3-3.1 Relating Parallel and Perpendicular Lines 23. ANS: C OBJ: 3-4.2 Using Exterior Angles of Triangles 24. ANS: B OBJ: 3-4.2 Using Exterior Angles of Triangles 25. ANS: A OBJ: 3-7.2 Slope and Perpendicular Lines 26. ANS: D OBJ: 3-1.2 Properties of Parallel Lines 27. ANS: B OBJ: 3-1.2 Properties of Parallel Lines

28. ANS: C OBJ: 3-4.2 Using Exterior Angles of Triangles 29. ANS: C OBJ: 3-6.1 Graphing Lines

30. ANS: C OBJ: 3-6.2 Writing Equations of Lines 31. ANS: C OBJ: 3-6.2 Writing Equations of Lines 32. ANS: B OBJ: 3-7.1 Slope and Parallel Lines

33. ANS: D OBJ: 3-7.2 Slope and Perpendicular Lines

34. ANS: D OBJ: 3-7.2 Slope and Perpendicular Lines

SHORT ANSWER

35. ANS:

a. Corresponding angles.

b. Vertical angles.

c. Transitive Property.

OBJ: 3-1.2 Properties of Parallel Lines

36. ANS:

a. Vertical angles.

b. Transitive Property.

c. Alternate Interior Angles Converse.

OBJ: 3-2.1 Using a Transversal