2. Write the point-slope form of the equation of the line passing through the point ( 2, 4) with a slope of 3. (1 point)

Transcription

1 Parallel and Perpendicular Lines Unit Test David Strong is taking this assessment. Multiple Choice 1. Which construction is illustrated above? a segment congruent to a given segment an angle congruent to a given angle the perpendicular bisector of a given segment the angle bisector of a given angle 2. Write the point-slope form of the equation of the line passing through the point ( 2, 4) with a slope of 3. y + 4 = 3(x 2) y 4 = 3(x 2) y + 4 = 3(x + 2) y 4 = 3(x + 2) 3. Write the equation for the horizontal line that contains point G( 8, 8). y = 8 x = 8 y = 1x + 8 y = 8 1/11

2 4. Find the value of x and y. x = 15, y = 12 x = 14, y = 11 x = 14, y = 12 x = 15, y = What is the relationship between 8 and 4? corresponding angles alternate exterior angles same-side interior angles alternate interior angles 2/11

3 6. Which construction is illustrated above? a perpendicular to a given line from a point on the line a line segment congruent to a given line segment a perpendicular to a given line from a point not on the line the perpendicular bisector of an angle 7. Which lines are parallel if m 5 = m 6? Justify your answer. line p is parallel to line q; converse of alternate interior angles theorem line p is parallel to line q; converse of corresponding angles postulate line l is parallel to line m; converse of corresponding angles postulate line p is parallel to line q; converse of same-side interior angles theorem 8. Write the equation for the vertical line that passes through the point (1, 1). x = 1 x = y y = 1 y = x 9. Which lines are parallel if m 1 + m 2 = 180? Justify your answer. 3/11

4 9. Which lines are parallel if m 1 + m 2 = 180? Justify your answer. j k by the converse of the same-side interior angles theorem j k by the converse of the alternate interior angles theorem g h by the converse of the alternate interior angles theorem g h by the converse of the same-side interior angles theorem 10. Which illustrates the construction of a perpendicular to a line from a point not on the line? 4/11

5 11. Find the value of x so that line m is parallel to line l /11

6 12. Write the equation of the line that passes through the points ( 2, 7) and (5, 7) in slope-intercept form. y = 2x 3 y = 2x + 3 y = 2x 3 y = 2x Find the value of x so that f(x) is parallel to g(x) Which two lines are parallel? I. 4y = 3x + 1 II. 4y = 3x 1 III. 3y = 4x 1 II and III I and III I and II No two of the lines are parallel. 15. Find the value of x for which l is parallel to m. The diagram is not to scale. 6/11

7 Is the line passing through points A( 5, 2) and B(2, 2) perpendicular to the line passing through points C(0, 5) and D(4, 12)? Yes, their slopes are different. No, their slopes are not opposite reciprocals. No, their slopes are not the same. Yes, their slopes are opposite reciprocals. 17. The folding chair has different settings that change the angles formed by its parts. Suppose m 2 is 31 and m 3 is 72. Find m 1. The diagram is not to scale Which of the following is the equation of the line passing through points A( 5, 2) and B(0, 8)? y = 2x + 8 y = 2x + 8 y = 2x 8 7/11

8 y = 2x Find the values of x, y, and z. x = 70, y = 110, z = 53 x = 80, y = 100, z = 63 x = 85, y = 95, z = 58 x = 80, y = 100, z = What is the graph of 3x 8y = 24? 8/11

9 21. Is the line through the points R( 1, 3) and S(2, 7) parallel to the graph of the line given by the equation, 10x+3y = 6? No, the slopes have opposite signs. Yes, the slopes have the same sign and value. Yes, the lines both decrease to the right. No, the lines have unequal slopes. 22. What is the slope of the line passing through the points A( 5, 7) and B(4, 7)? undefined Which pair of angles are corresponding angles? 9/11

10 1 and 2 1 and 5 2 and 7 2 and Complete the two-column proof. Given: 2 and 5 are supplementary Prove: Statements Reasons and 5 are supplementary /11

11 (6 points) 11/11