Student:
Class:
Date:
Lines and transversals
Student Activity Sheet 3; use with Exploring “Other angles”
1. REVIEW Use what you know about corresponding angles, vertical angles, and linear pairs
to find the measure of each angle labeled in the diagram, given that line l is parallel to
line m.
30°
6
7
5
2
1
l
3
4
m
2. Identify all pairs of alternate interior angles in the diagram below.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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With space for student work.
Student:
Class:
Date:
Lines and transversals
Student Activity Sheet 3; use with Exploring “Other angles”
3. Write a definition for alternate interior angles.
4. Write a conjecture about the relationship between the alternate interior angles formed
by two parallel lines cut by a transversal.
5. Use the given tiles to fill in the blanks and complete the proof.
∠3 ≅ ∠6
alternate
interior
Statements
∠3 ≅ ∠2
corresponding
Given
∠2 ≅ ∠6
Reasons
1. j  k
1. _________________________________
2. _____________
2. Vertical angles are congruent.
3. _____________
3. If parallel lines are cut by a transversal,
____________________ angles are congruent.
4. _____________
4. Transitive Property of Congruence
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
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With space for student work.
Student:
Class:
Date:
Lines and transversals
Student Activity Sheet 3; use with Exploring “Other angles”
6. Identify all pairs of consecutive interior angles in the diagram.
7. What is another name for consecutive interior angles?
8. If two parallel lines are cut by a transversal, does it appear to be true that the
consecutive interior angles are congruent?
9. Write a conjecture about the relationship between the consecutive interior angles
formed by two parallel lines cut by a transversal.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 3 of 5
With space for student work.
Student:
Class:
Date:
Lines and transversals
Student Activity Sheet 3; use with Exploring “Other angles”
10. Use the given tiles to fill in the blanks and complete the proof.
m∠6 + m∠4 = 180
parallel lines are
congruent
jk
Definition of
congruent angles
Linear Pair
Theorem
Lines j and k are parallel.
Prove that the sum of the
consecutive interior angles
formed by parallel lines is
180°.
Statements
1. ____________________
2. ∠2 ≅ ∠6
Reasons
1. Given
2. Corresponding angles formed by
__________________________________.
3. m∠2 = m∠6
3. ___________________________________
4. m∠2 and m∠4 form a linear pair.
4. Definition of linear pair.
4. m∠2 + m∠4 = 180
4. ___________________________________
5. ____________________
5. Substitution
11. When two lines are cut by a transversal, how many pairs of each of the following types of
angles are formed?
a. Corresponding angles:
____ pairs
b. Alternate interior angles:
____ pairs
c. Consecutive interior angles:
____ pairs
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 5
With space for student work.
Student:
Class:
Date:
Lines and transversals
Student Activity Sheet 3; use with Exploring “Other angles”
12. REINFORCE Given l || m, find the measure of each measured angle in the diagram.
1
(3x2 + 10)°
(3x2 + 10)°
2
3
(9x + 50)°
(9x+50)°
4
6
l
m
5
13. REINFORCE When are the alternate interior angles formed by two lines cut by a
transversal not congruent?
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 5 of 5
With space for student work.