NAME _____________________________________________ DATE ____________________________ PERIOD _____________
3-1 Study Guide and Intervention
Parallel Lines and Transversals
Relationships Between Lines and Planes When two lines lie in the same plane and
do not intersect, they are parallel. Lines that do not intersect and are not coplanar are
̅̅̅̅.
skew lines. In the figure, ℓ is parallel to m, or ℓ || m. You can also write ̅̅̅̅
𝑃𝑄 || 𝑅𝑆
Similarly, if two planes do not intersect, they are parallel planes.
Exercises
Refer to the figure at the right to identify each of the following.
1. all planes that intersect plane OPT
̅̅̅̅
2. all segments parallel to 𝑁𝑈
3. all segments that intersect ̅̅̅̅̅
𝑀𝑃
Refer to the figure at the right to identify each of the following.
4. all segments parallel to ̅̅̅̅
𝑄𝑋
5. all planes that intersect plane MHE
6. all segments parallel to ̅̅̅̅
𝑄𝑅
̅̅̅̅
7. all segments skew to 𝐴𝐺
Angle Relationships A line that intersects two or more other lines at two different points in a plane is called a
transversal. In the figure below, line t is a transversal. Two lines and a transversal form eight angles. Some pairs of the
angles have special names. The following chart lists the pairs of angles and their names.
Angle Pairs
Name
∠3, ∠4, ∠5, and ∠6
interior angles
∠3 and ∠5; ∠4 and ∠6
alternate interior angles
∠3 and ∠6; ∠4 and ∠5
consecutive interior angles
∠1, ∠2, ∠7, and ∠8
exterior angles
∠1 and ∠7; ∠2 and ∠8;
alternate exterior angles
∠1 and ∠5; ∠2 and ∠6;
∠3 and ∠7; ∠4 and ∠8
corresponding angles
Chapter 3
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Example: Classify the relationship between each pair of angles as alternate
interior, alternate exterior, corresponding, or consecutive interior angles.
a. ∠10 and ∠16
b. ∠4 and ∠12
alternate exterior angles
corresponding angles
c. ∠12 and ∠13
d. ∠3 and ∠9
consecutive interior angles
alternate interior angles
Exercises
Use the figure in the Example for Exercises 1-12.
Identify the transversal connecting each pair of angles.
1. ∠9 and ∠13
2. ∠5 and ∠14
3. ∠4 and ∠6
Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or
consecutive interior angles.
4. ∠1 and ∠5
5. ∠6 and ∠14
6. ∠2 and ∠8
7. ∠3 and ∠11
8. ∠12 and ∠3
9. ∠4 and ∠6
3-2 Study Guide and Intervention
Angles and Parallel Lines
Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal, the following pairs of angles are
congruent.
• corresponding angles
• alternate interior angles
• alternate exterior angles
Also, consecutive interior angles are supplementary.
In the figure, m∠ 9 = 80 and m∠ 5 = 68. Find the measure
of each angle. Tell which postulate(s) or theorem(s) you used.
1. ∠ 12
2. ∠ 1
3. ∠ 4
4. ∠ 3
5. ∠ 7
6. ∠ 16
Chapter 3
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Algebra and Angle Measures Algebra can be used to find unknown values in angles formed by a transversal and
parallel lines.
Exercises
Find the value of the variable(s) in each figure. Explain your reasoning.
1.
2.
3.
4.
Find the value of the variable(s) in each figure. Explain your reasoning.
5.
6.
3-3 Study Guide and Intervention
Slopes of Lines
Slope of a Line The slope m of a line containing two points with coordinates (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) is given by the
𝑦 −𝑦
formula m = 𝑥2 − 𝑥1 , where 𝑥1 ≠ 𝑥2 .
2
1
Exercises
Determine the slope of the line that contains the given points.
1. J(0, 0), K(–2, 8)
2. R(–2, –3), S(3, –5)
3. L(1, –2), N(–6, 3)
4. P(–1, 2), Q(–9, 6)
Chapter 3
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Find the slope of each line.
6. ⃡𝐴𝐵
7. ⃡𝐶𝐷
⃡
8. 𝐸𝑀
9. ⃡𝐴𝐸
Parallel and Perpendicular Lines If you examine the slopes of pairs of parallel lines and the slopes of pairs of
perpendicular lines, where neither line in each pair is vertical, you will discover the following properties.
Two lines have the same slope if and only if they are parallel.
Two lines are perpendicular if and only if the product of their slopes is –1.
Exercises
⃡ are parallel, perpendicular, or neither. Graph each line to verify your answer.
⃡
Determine whether 𝑴𝑵
and 𝑹𝑺
1. M(0, 3), N(2, 4), R(2, 1), S(8, 4)
2. M(–1, 3), N(0, 5), R(2, 1), S(6, –1)
Graph the line that satisfies each condition.
3. slope = 4, passes through (6, 2)
4. passes through H(8, 5), perpendicular to ⃡𝐴𝐺 with A(–5, 6) and G(–1, –2)
5. passes through C(–2, 5), parallel to ⃡𝐿𝐵 with L(2, 1) and B(7, 4)
Chapter 3
Glencoe Geometry