Download Name: Date: Period - Effingham County Schools

Name:
Date:
Period:
.
Practice A 3.1: Angles Formed by Parallel Lines and Transversals
1. The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then the pairs
of corresponding angles are ____________________.
2. Congruent angles have _____________________ measures.
Find each angle measure.
3.m1 _______________________
4. m2 _______________________
Find x.
5.
6.
________________________________________
________________________________________
Fill in the blanks to complete these theorems about angle pairs.
7. If two _____________________ lines are cut by a _____________________, then the two pairs of
alternate interior angles are congruent.
8. If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are
_____________________.
9. If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are
_____________________.
Practice B 3.1: Angles Formed by Parallel Lines and Transversals
1. m1 _______________________
2. m2 _______________________
Find each angle measure.
3. mABC _______________________
4. mDEF _______________________
Complete the two-column proof, using the Proof Bank, to show that same-side exterior angles are
supplementary. Hint: Draw a picture first.
5. Given: p || q
Proof Bank:
Prove: m1  m3  180
Proof:
Subst.
Statements
Reasons
1. p || q
1. Given
2. a. _______________________
2. Lin. Pair Thm.
Corr. s Post.
m2 + m3 = 180°
m1 = m2
m1 + m3 = 180°
3. 1  2
3. b. _______________________
4. c. _______________________
4. Def. of  s
5. d. _______________________
5. e. _______________________
Problem Solving 3.1: Angles Formed by Parallel Lines and Transversals
Find each value. Name the postulate or theorem that you used to find the values.
1. In the diagram of movie theater seats,
the incline of the floor, f, is parallel to
the seats, s.
If m168, what is x?
________________________________________
2. In the diagram, roads a and b are parallel.
What is the measure of PQR?
________________________________________
Use the diagram of a staircase railing for Exercises 4 and 5. AG || CJ and AD || FJ .
Choose the best answer.
3. Which is a true statement about the measure of DCJ?
A It equals 30, by the Alternate Interior Angles Theorem.
B It equals 30, by the Corresponding Angles Postulate.
C It equals 50, by the Alternate Interior Angles Theorem.
D It equals 50, by the Corresponding Angles Postulate.
4.Which is a true statement about the value of n?
F It equals 25, by the Alternate Interior Angles Theorem.
G It equals 25, by the Same-Side Interior Angles Theorem.
H It equals 35, by the Alternate Interior Angles Theorem.
J It equals 35, by the Same-Side Interior Angles Theorem.
Practice A 3.2
Proving Lines Parallel
1. The Converse of the Corresponding Angles Postulate states that if two coplanar lines are cut by a
transversal so that a pair of corresponding angles is congruent, then the two lines are
____________________.
Use the figure for Exercises 2 and 3. Given
the information in each exercise, state the
reason why lines b and c are parallel.
2. 4  8
3. m368, m7(5x3), x13
________________________________________
_________________________________________
________________________________________
_________________________________________
Fill in the blanks to complete these theorems about parallel lines.
4. If two coplanar lines are cut by a ______________________ so that a pair of alternate interior angles are
______________________, then the two lines are parallel.
5. If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are
______________________, then the two lines are parallel.
6. If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then
the two lines are ______________________.
7. Shu believes that a theorem is missing from the lesson. His conjecture is that if two coplanar lines are cut
by a transversal so that a pair of same-side exterior angles are supplementary, then the two lines are
parallel. Complete the two-column proof with the statements and reasons provided.
m || n
2 and 3 are supplementary.
Given
 Supps. Thm.
Given: 1 and 3 are supplementary.
Prove: m || n
Proof:
Statements
Reasons
1. 1 and 3 are supplementary.
1. a. ___________________________
2. b. ___________________________
2. Linear Pair Thm.
3. 1  2
3. c. ___________________________
4. d. ___________________________
4. Conv. of Corr. s Post.
Problem Solving 3.2
Proving Lines Parallel
1. A bedroom has sloping ceilings as shown. Marcel is hanging
a shelf below a rafter. If m1(8x  1), m2(6x7),
and x4, show that the shelf is parallel to the rafter above it.
2. In the sign, m3(3y7), m4(5y5), and y21.
Show that the sign posts are parallel.
Choose the best answer.
3. In the bench, mEFG(4n16), mFJL(3n40),
mGKL(3n22), and n24. Which is a true statement?
A FG || HK by the Converse of the Corr. s Post.
B FG || HK by the Converse of the Alt. Int. s Thm.
C EJ || GK by the Converse of the Corr. s Post.
D EJ || GK by the Converse of the Alt. Int. s Thm.
4.In the windsurfing sail, m5(7c1), m6(9c  1),
m717c, and c6. Which is a true statement?
F RV is parallel to SW .
G SW is parallel to TX .
H RT is parallel to VX .
J Cannot conclude that two segments are parallel
The figure shows Natalia’s initials, which are
monogrammed on her duffel bag. Use the
figure for Exercises5and 6.
5. If m1(4x  24), m2(2x8),
and x16, show that the sides of
the letter N are parallel.
6. If m3(7x13), m4(5x35),
and x11, show that the sides of the
letter H are parallel.
________________________________________
_________________________________________
Practice A 3.3
Perpendicular Lines
1. The perpendicular bisector of a segment is a line ______________________
to a segment at the segment’s ______________________.
2. The shortest segment from a point to a line is ______________________ to the line.
For Exercises 3 and 4, name the shortest segment from the point to the line and
write an inequality for x.
3.
4.
________________________________________
________________________________________
Fill in the blanks to complete these theorems about parallel and
perpendicular lines.
5. If two coplanar lines are perpendicular to the same line, then the two lines are ______________________
to each other.
6. If two intersecting lines form a linear pair of ______________________ angles,
then the lines are perpendicular.
7. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is
______________________ to the other line.
Practice B 3.3
Perpendicular Lines
For Exercises 1–4, name the shortest segment from the point to the line and
write an inequality for x.
1.
2.
________________________________________
________________________________________
3.
________________________________________
Complete the two-column proof using the Proof Bank.
4. Given: m  n
Prove: 1 and 2 are a linear pair of congruent angles.
Proof Bank:
Proof:
Statements
Reasons
1. a. ___________________________
1. Given
2. b. ___________________________
2. Def. of 
3. 1  2
3. c. ___________________________
4. m1m2180
4. Add. Prop. of 5
5. d. ___________________________
5. Def. of linear pair
1 and 2 are a linear
pair.
Def. of  s
m1  90°, m2  90°
mn