Choose the correct response using the diagram at the right..
1. corresponding angles:
a) ∠14 and ∠3
b) ∠12 and ∠10 c) ∠1 and ∠6 d) ∠16 and ∠12
2. exterior angles :
a) ∠14 and ∠3
b) ∠12 and ∠10 c) ∠1 and ∠6 d) ∠16 and ∠12
3. What type of angle pair are ∠7 and ∠10 ?:
a) alternate interior angles b) alternate exterior angles c) same-side interior d) corresponding angles
4. If 𝑐 ∥ 𝑑, then ∠6 ≅ ∠12 by what theorem?___________________________________________
5. If 𝑚∠11 + 𝑚∠10 = 180 , then line _____ is parallel to line _______ by the _______________________
Theorem.
For problems 6-8, use the diagram to find and state theorem or postulate that justifies your answer.
.
6.
7.
.
8.
m∠1 = ________
m∠1 = ____________
m∠1 = _________
justify:_________
justify:___________
justify:___________
m∠2 = _________
m∠2= _____________
m∠2= _____________
justify: _________
justify:____________
justify:____________
9. Use the given information to determine which lines are parallel and justify with a theorem or postulate.
a) Given: 𝑚∠6 ≅ 𝑚∠7
Conclusion: _______ by ________________________
b) Given: 𝑚∠3 ≅ 𝑚∠13
Conclusion: _______ by ________________________
b) Given: 𝑚∠5 ≅ 𝑚∠11
Conclusion: _______ by ________________________
10. Find the value of the variable x.
a)
b)
11. For the following constructions, show all compass marks.
a) Construct the line parallel to m through Q.
b) Construct a quadrilateral ABCD.
̅̅̅̅̅|| 𝐶𝐷
̅̅̅̅ and AB = a and CD = b.
Given: 𝐴𝐵
In problems 12-14, find the values of the variables.
12.
13.
14.
15. What is the interior angle sum of a convex 35-gon?
16. What is the interior angle sum of this polygon?
Determine whether the following pairs of lines are parallel, perpendicular, or neither.
17.
18.
19.
Write the equation of each line described.
20. The line has slope of 6 and contains
.
21. The line is perpendicular to
and contains
22. The line passes through (6, 4) and
.
Using intercepts, graph each of the following.
23.
Find the slope of
and
.
24.
. Then determine whether
and
are parallel, perpendicular, or
neither. Explain.
25. L(10, 2),
Q(10, 6), R(9, 4)
26.
Q(14, 16), R(10, 4)