Download Worksheet on Parallel Lines and Transversals

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Geometry 22: Even MORE Practice Chapter 3
1. Match each term with its mathematical meaning.
A. transversal
I. two angles whose measures have a sum of 180
B. complementary angles
II. Two coplanar lines that never intersect
C. skew lines
III. Two non-coplanar lines that never intersect
D. parallel lines
IV. A line that intersects two or more coplanar lines at two distinct points
E. supplementary angles
V. two angles whose measures have a sum of 90
2. Identify the following in the diagram at the right.
a. two lines that are parallel to plane FGI
suur
b. two lines that are parallel to HL

c. two lines that are skew to FG
d. a pair of parallel planes
e. the intersection of plane LMK and plane IGK
3. In the problems below, find the value of x.
a.
b.
m1   3 x  17  
2
m2   x  1 
1
m1   95  7 x  
1
2
m2   55  x  
4. Use the given informatin to determine which lines, if any, are parallel. Justify each conclusion with
a theorem or postulate.
a. ∠ 6 is supplementary to ∠ 10
b. ∠ 3 ≅ ∠ 8
c. ∠5 is supplementary to ∠ 1
d. ∠ 2 ≅ ∠ 7
e. ∠ 4 ≅ ∠ 11
f. ∠ 9 ≅ ∠ 1
5. In the diagram below, find the missing angle measures.
m1  _______
m2  _______
m3  _______
m4  _______
m5  _______
m6  _______
m7  _______
m8  _______
m9  _______
m10  _______
m11  _______
m12  _______
6. Given that l m , find the value(s) of x and each angle. Be sure to check for extraneous
solutions.
a.
b.
m3   x 2  112  
m8  16 x  131 
m1   x 2  7 x  
m7    x  7  
7. Find the missing angle measure in the images below. Note: Drawings are NOT to scale.
a.
b.
8. In a triangle, 1 is an exterior angle and 2 and 3 are its remote interior angles. Find the measures of 2
and 3, given that m1 = 150, m2 = 2x + 3, and m3 = 5x + 7. Sketch the image if necessary.
9. Find m1.
a.
b.
c.
10. Find the value of each variable.
a.
b.
c.
8. Complete the following fill-in proofs.
a. Given: m n
Prove: m1  m7  180
1.
2.
3.
4.
5.
6.
7.
8.
STATEMENTS
m n
1 and 5 are Corresponding Angles
1  5
m1  m5
5 and 7 are a linear pair
REASONS
1.
2.
3.
4.
5.
6. Linear Pair Postulate
7.
8.
m5  m7  180
b. Given: AB CD
;
3  1
Prove: EF GH
STATEMENTS
1.
2.
3.
4.
5.
6.
REASONS
4 and 2 are alternate interior angles
4   2
3  1
m3  m1
mEFG  m3  m4
7.
mHGF  m1  m2
8. mEFG  m1 m2
9. mEFG  mHGF
10.
11. EFG and HGF are alternate interior angles
12.
1. Given
2.
3.
4. Definition of congruence
5.
6.
7.
8.
9.
10. Definition of congruence
11.
12.
c. Given: AB  CD
Prove: 1 and 2 are complementary angles
STATEMENTS
1.
2. 3 is a right angle
3.
4. m1  m2  m3  180
5. m1  m2  90  180
6.
7.
REASONS
1. Given
2.
3. Definition of right angle
4.
5.
6. Subtraction Property of Equality
7.