Geo - CH3 Prctice Test

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1 Geo - CH3 Prctice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the transversal and classify the angle pair 11 and 7. a. The transversal is line l. The angles are corresponding angles. b. The transversal is line l. The angles are alternate interior angles. c. The transversal is line n. The angles are alternate exterior angles. d. The transversal is line m. The angles are corresponding angles. 2. Draw two lines and a transversal such that 1 and 2 are alternate interior angles, 2 and 3 are corresponding angles, and 3 and 4 are alternate exterior angles. What type of angle pair is 1 and 4? a. b. 1 and 4 are supplementary angles. 1 and 4 are corresponding angles.

2 c. d. 1 and 4 are vertical angles. 1 and 4 are alternate exterior angles. 3. Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two transversals to the violin strings. Find x and y in the diagram. a. x = 10, y = 20 c. x = 0, y = 60 b. x = 20, y = 20 d. x = 10, y = Use the Converse of the Corresponding Angles Postulate and 1 2 to show that l Ä m. a. 1 2 is given. From the diagram, 1 and 2 are alternate interior angles. So by the Converse of the Alternate Interior Angles Postulate, l Ä m.

3 b. 1 2 is given. From the diagram, 1 and 2 are corresponding angles. So by the Converse of the Corresponding Angles Postulate, l Ä m. c. 1 2 is given. From the diagram, 1 and 2 are corresponding angles. So by the Corresponding Angles Postulate, l Ä m. d. By the Converse of the Corresponding Angles Postulate, 1 2. From the diagram, l Ä m. 5. Write and solve an inequality for x. a. x > 2 c. x > 1 b. x < 2 d. x < 2 6. Write a two-column proof. Given: t l, 1 2 Prove: m Ä l Complete the proof. Proof: Statements 1. [1] 1. Given 2. t m 2. [2] 3. m Ä l 3. [3] Reasons a. [1] t l, 1 2 [2] 2 intersecting lines form linear pair of s lines. [3] 2 lines to the same line lines Ä. b. [1] t l, 1 2 [2] 2 lines to the same line lines Ä. [3] 2 intersecting lines form linear pair of s lines. c. [1] t l, 1 2 [2] 2 intersecting lines form linear pair of s lines.

4 [3] Perpendicular Transversal Theorem d. [1] t l, 1 2 [2] Perpendicular Transversal Theorem [3] 2 lines to the same line lines Ä. 7. Milan starts at the bottom of a 1000-foot hill at 10:00 am and bikes to the top by 3:00 PM. Graph the line that represents Milan s distance up the hill at a given time. Find and interpret the slope of the line. a. b. The slope is 200, so Milan traveled 200 feet per hour. c. The slope is , so Milan traveled 7 feet per hour. d. The slope is 1 200, so Milan traveled feet per hour. The slope is 7 200, so Milan travels feet per hour. 8. AB Ä CD for A(4, 5), B( 2, 3), C(x, 2), and D(6, y). Find a set of possible values for x and y. a. Ï Ê Ì Á Ë x, y ˆ y = 1 3 x 4, x 6 c. Ï ÓÔ Ì Ê x, y Ô Ë Á ˆ y = 3x 20, y 2 ÓÔ Ô

5 b. Ï Ì Ê Ë Á x, y ˆ y = 1 3 x 4 ÓÔ d. Ô 9. Graph the line y 3 = 4(x 6). a. c. Ï Ê Ì Ë Á x, y ˆ y = 3x 20, x 2 ÓÔ Ô b. d. 10. Determine whether the pair of lines 12x + 3y = 3 and y = 4x + 1 are parallel, intersect, or coincide. a. intersect c. parallel b. coincide Numeric Response 11. Find the value of x so that m Ä n.

6 12. A right triangle is formed by the x-axis, the y-axis and the line y = 2x + 3. Find the length of the hypotenuse. Round your answer to the nearest hundredth. Matching Match each vocabulary term with its definition. a. vertical angles b. alternate interior angles c. corresponding angles d. supplementary angles e. transversal f. same-side interior angles g. alternate exterior angles 13. a line that intersects two coplanar lines at two different points 14. for two lines intersected by a transversal, a pair of angles that are on the same side of the transversal and between the two lines 15. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and outside the other two lines 16. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and between the other two lines Match each vocabulary term with its definition. a. x-intercept b. point-slope form c. rise d. run e. y-intercept f. distance from a point to a line g. slope-intercept form h. slope 17. y y 1 = m(x x 1 ), where m is the slope and (x 1, y 1 ) is a point on the line 18. the difference in the y-values of two points on a line 19. a line with slope m and y-intercept b can be written in the form y = mx + b 20. a measure of the steepness of a line

7 21. the length of the perpendicular segment from the point to the line 22. the difference in the x-values of two points on a line

8 Geo - CH3 Prctice Test Answer Section MULTIPLE CHOICE 1. ANS: A To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. Corresponding angles lie on the same side of the transversal l, on the same sides of lines n and m. A B C D Alternate interior angles lie on opposite sides of the transversal, between two lines. To find which line is the transversal for a given angle pair, locate the line that connects the vertices. To find which line is the transversal for a given angle pair, locate the line that connects the vertices. PTS: 1 DIF: Average REF: Page 147 OBJ: Identifying Angle Pairs and Transversals NAT: g TOP: 3-1 Lines and Angles 2. ANS: B Step 1 Draw two lines m, n, and a transversal p such that 1 and 2 are alternate interior angles. They should lie on opposite sides of the transversal p between lines m and n. Step 2 2 and 3 are corresponding angles. Corresponding angles lie on the same side of the transversal p and on the same sides of lines m and n. Add 3 to the drawing. Step 3 3 and 4 are alternate exterior angles. They should lie on opposite sides of the transversal p and outside lines m and n. Add 4 to the drawing. 1 and 4 are corresponding angles. They lie on the same side of the transversal p and on the same sides of lines m and n.

9 A B C D Angles 2 and 3 are corresponding angles and should lie on the same side of transversal p, on the same sides of lines m and n. Angles 2 and 3 are corresponding angles and should lie on the same side of transversal p, on the same sides of lines m and n. Angles 1 and 2 are alternate interior angles and should lie on opposite sides of transversal p, between lines m and n. PTS: 1 DIF: Advanced NAT: f TOP: 3-1 Lines and Angles KEY: multi-step 3. ANS: A By the Corresponding Angles Postulate, (4x + y) = 60. By the Alternate Interior Angle Postulate, (8x + y) = x + y = 100 (4x + y) = 60 Subtract the first equation from the second. 4x = 40 x = 10 Divide both sides by 4. 8(10) + y = 100 Substitute 10 for x. y = 20 Simplify. A B C D When solving a system of two equations, subtract the second equation from the first. Use postulates related to parallel lines to form two equations. When solving a system of two equations, subtract the second equation from the first. PTS: 1 DIF: Advanced REF: Page 157 OBJ: Application NAT: g TOP: 3-2 Angles Formed by Parallel Lines and Transversals 4. ANS: B

10 1 2 is given. From the diagram, 1 and 2 are corresponding angles. So by the Converse of the Corresponding Angles Postulate, l Ä m. A B C D Use the Converse of the Corresponding Angles Postulate. Use the Converse of the Corresponding Angles Postulate. Use the given information. PTS: 1 DIF: Basic REF: Page162 OBJ: Using the converse of the Corresponding Angles Postulate NAT: g TOP: 3-3 Proving Lines Parallel 5. ANS: A DA > DC DC is the shorter segment. 2x + 4 > 8 Substitute 2x + 4 for DA and 8 for DC. 2x > 4 Subtract 4 from both sides. x > 2 Divide both sides by 2 and simplify. A B Change the inequality sign. C Check your simplification methods. D Do not change the inequality sign when subtracting 4 or dividing by 2. PTS: 1 DIF: Average REF: Page 172 OBJ: Distance From a Point to a Line NAT: a TOP: 3-4 Perpendicular Lines 6. ANS: A Proof: Statements Reasons 1. t l, Given 2. t m 2. If 2 intersecting lines form linear pair of s lines. 3. m Ä l 3. If 2 lines to the same line lines Ä. A B Switch Reason 2 and Reason 3. C Reason 2 is if 2 intersecting lines form a linear pair of congruent angles, then the lines are perpendicular. Reason 3 is if 2 lines are perpendicular to the same line, then the lines are parallel. D Reason 2 is if 2 intersecting lines form a linear pair of congruent angles, then the

11 lines are perpendicular. Reason 3 is if 2 lines are perpendicular to the same line, then the lines are parallel. PTS: 1 DIF: Basic REF: Page 173 OBJ: Proving Properties of Lines NAT: a TOP: 3-4 Perpendicular Lines 7. ANS: A Convert 3:00 pm to 15:00. Use the points (10, 0) and (15, 1000) to make the graph and find the slope. m = = = 200 The slope is 200, which means Milan is traveling at 200 feet per hour. A B C D Convert 3:00pm to 15:00, then solve for the slope. The slope is the distance traveled divided by the time elapsed. Convert 3:00pm to 15:00, then solve for the slope. PTS: 1 DIF: Average REF: Page 183 OBJ: Application NAT: a TOP: 3-5 Slopes of Lines 8. ANS: A 3 ( 5) slope of AB = = = 1 3 slope of CD = y ( 2) = y x 6 x, x 6 y x = 1 Parallel lines have the same slope. Write an equation 3 comparing the slopes of AB and CD. 3(y + 2) = 1(6 x) Cross multiply. 3y 6 = 6 x Distribute. 3y = 12 x Simplify. y = 1 3 x 4 The set of possible values for x and y is Ï Ì Ê Ë Á x, y ˆ y = 1 3 x 4, x 6 ÓÔ Ô Ô. A

12 B Check the constraints of x. C In the slope formula, the difference of the y-values is in the numerator and the difference of the x-values in the denominator. D First, find the slopes of the segments. Then, set the slopes equal to each other and cross multiply and simplify. PTS: 1 DIF: Advanced NAT: g TOP: 3-5 Slopes of Lines 9. ANS: B The equation is given in point-slope form y y 1 = m(x x 1 ). The slope is m = 4 = 4 1 and the coordinates of a point on the line are (6, 3). Plot the point (6, 3) and then rise 4 and run 1 to locate another point. Draw the line connecting the two points. A B C D The equation is of the form y b = m(x a), so the graph passes through the point (a, b). The equation is of the form y b = m(x a), so the graph passes through the point (a, b). The equation is of the form y b = m(x a), so the graph passes through the point (a, b). PTS: 1 DIF: Average REF: Page 191 OBJ: Graphing Lines NAT: a TOP: 3-6 Lines in the Coordinate Plane 10. ANS: A Solve the first equation for y to find the slope-intercept form. Compare the slopes and y-intercepts of both equations. 12x + 3y = 3 3y = 12x + 3 y = 4x + 1

13 y = 4x + 1 The slope of the first equation is 4 and the y-intercept is 1. The slope of the second equation is 4 and the y-intercept is 1. The lines have different slopes, so they intersect. A B C Write both lines in slope-intercept form and compare. Write both lines in slope-intercept form and compare. PTS: 1 DIF: Average REF: Page 192 OBJ: Classifying Pairs of Lines NAT: a TOP: 3-6 Lines in the Coordinate Plane NUMERIC RESPONSE 11. ANS: 17 PTS: 1 DIF: Average NAT: f TOP: 3-3 Proving Lines Parallel 12. ANS: 3.35 PTS: 1 DIF: Advanced NAT: d TOP: 3-6 Lines in the Coordinate Plane MATCHING 13. ANS: E PTS: 1 DIF: Basic REF: Page 147 TOP: 3-1 Lines and Angles 14. ANS: F PTS: 1 DIF: Basic REF: Page 147 TOP: 3-1 Lines and Angles 15. ANS: G PTS: 1 DIF: Basic REF: Page 147 TOP: 3-1 Lines and Angles 16. ANS: B PTS: 1 DIF: Basic REF: Page 147 TOP: 3-1 Lines and Angles 17. ANS: B PTS: 1 DIF: Basic REF: Page 190 TOP: 3-6 Lines in the Coordinate Plane 18. ANS: C PTS: 1 DIF: Basic REF: Page 182 TOP: 3-5 Slopes of Lines 19. ANS: G PTS: 1 DIF: Basic REF: Page 190 TOP: 3-6 Lines in the Coordinate Plane 20. ANS: H PTS: 1 DIF: Basic REF: Page 182

14 TOP: 3-5 Slopes of Lines 21. ANS: F PTS: 1 DIF: Basic REF: Page 172 TOP: 3-4 Perpendicular Lines 22. ANS: D PTS: 1 DIF: Basic REF: Page 182 TOP: 3-5 Slopes of Lines

GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5)

Name: Class: Date: SHOW ALL WORK GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5) Match each vocabulary term with its definition. (#1-5) a. parallel lines b. parallel planes c. perpendicular lines d. skew