Download Topic 3 Test Review

Name
Class
Date
Topic 3 Test Review
Use the figure for Exercises 1-8.
For Exercises 1–8, suppose a || b and c || d.
1. 2 and 10 are what kind of angles?
2. 3 and what angle are alternate interior angles?
3. 9 and 8 are what kind of angles?
4. Which angle could you show is congruent to 11 to prove a || b?
5. What relationship between 6 and 11 to shows c || d?
6. If m6  50 , then find m11 .
7. If m2  70 , then find m6 .
8. If m1  130 , then find m5 .
9. Suppose a line intersecting two lines a and b forms a 35° angle with each line. What are
the possible relationships between lines a and b? Explain. (Hint: Draw a picture.)
10. Find the value of the variables in the triangle at
the right.
11. Explain how perpendicular lines can be used to
construct a line parallel to a given line.
12. Find the slope of the line passing through (–6, –2) and (–3, –6).
13. Find the equation of the line with a slope 6 and y-intercept 4.
14. Find the equation of the line passing through (10, 2) and (2, –2).
Name
Class
Date
Topic 3 Test (continued)
15. A triangle has 1 and 2 as remote interior angles with respect to exterior angle 3 .
Given that m1  50 and m2  70 , Alicia reasoned that m3 must be 60. Explain
Alicia’s error.
Determine whether the following pairs of lines are parallel, perpendicular, or neither.
16. y = 2x + 1
2x + y = 7
17. y =
1
3
18. y = –4x + 1
x+4
4x + y = –3
3x + y = 2
19. What is the equation of the line parallel to y = x – 1 that contains the point (1, 2)?
20. What is the equation of the line perpendicular to y =
1
2
x + 1 that contains the point
(–2, 1)?
Classify each set of angle measures as the angle measures of a triangle in Euclidean
geometry, a triangle in spherical geometry, or neither.
21. 28, 46, 75
22. 25, 45, 130
23. 22, 55, 103
24. Water Street intersects 25th Street and 28th Street at right angles. Highway 47 is parallel
to 28th Street. How are 25th Street and Highway 47 related? Explain.
For Exercises 25-26, determine whether each of the following properties of Euclidean
geometry is true in spherical geometry.
25. A line segment is the shortest distance between two points.
26. Through a point not on a line, there is one and only one line parallel to the given line.
27. Draw a line m and a point Q not on the line. Construct the line through Q parallel to
line m.