2. GUIDE CARD
LEAST LEARNED COMPETENCY
derives relationships among angles formed by parallel
lines cut by a transversal using measurement
OBJECTIVES
Illustrates parallel lines and a transversal
Identifies angles formed by parallel lines cut
by a transversal
Find the measures of angles formed by
parallel lines cut by a transversal
3. What are
PARALLEL LINES?
PARALLEL LINES are two lines which are
equidistant from each other and do not
meet
The symbol || is used to indicate
parallel lines.
A
B
D
C
AB || CD
4. What is a
TRANSVERSAL?
A TRANSVERSAL is
line, ray, or segment
that intersects 2 or
more COPLANAR lines,
rays, or segments.
transversal
5. ACTIVITY CARD #1
• Identify whether the RED line is transversal or
not. Write X if not and O if it is a transversal.
1. 2.
3. 4.
5.
6. Special Angle Relationships
Interior Angles
Angles that lie between
parallel lines on opposite
sides of the transversal.
1
4
2
65
7 8
3
Interior
Exterior
Exterior
∠3 and ∠6 are Alternate
Interior angles
∠4 and ∠5 are Alternate
Interior angles
∠3 and ∠5 are Same Side Interior angles
∠4 and ∠6 are Same Side Interior angles
7. Special Angle Relationships
1
4
2
65
7 8
3
Exterior Angles
angles that lie outside
parallel lines on opposite
sides of the transversal.Interior
Exterior
Exterior
∠1 and ∠8 are Alternate
Exterior angles
∠2 and ∠7 are Alternate
Exterior angles
∠1 and ∠7 are Same Side Exterior angles
∠2 and ∠8 are Same Side Exterior angles
8. Corresponding Angles
• Two angles that occupy corresponding
positions.
4
21
3
5 6
7 8
∠1 and ∠5
∠3 and ∠7
∠2 and ∠6
∠4 and ∠8
The corresponding angles are:
Special Angle Relationships
WHENTHE LINES ARE
PARALLEL
9. ACTIVITY CARD #2
• Name all angles being
asked based on the
figure.
1. Interior Angles
2. Exterior Angles
3. Alternate- Interior Angles
4. Alternate- Exterior
Angles
5. Corresponding Angles
6. Same side Interior
angles
7. Same side Exterior
Angles
10. Special Angle Relationships
WHEN THE LINES ARE PARALLEL
Alternate Interior Angles are
CONGRUENT1
4
2
65
7 8
3
If the lines are not
parallel, these angle
relationships DO NOT
EXIST.
Interior
Exterior
Exterior
Alternate Exterior Angles are
CONGRUENT
Same Side Interior Angles are
SUPPLEMENTARY
Same Side Exterior Angles are
SUPPLEMENTARY
11. ACTIVITY CARD #3
• Given the figure,
∠W=60° . Give the
measures of the
other angles.
12. ASSESSMENT CARD
I. Identify the angles formed by parallel lines cut by a
transversal.
1. ∠L and ∠Z
2. ∠B and ∠Z
3. ∠L and ∠N
4. ∠I and ∠R
5. ∠S and ∠A
6. ∠B and ∠N
7. ∠S and ∠N
8. ∠I and ∠Z
9. ∠S and ∠R
10. ∠L and ∠A
L
I Z A
S B R N
13. II. If m∠1=120°. Find all the remaining angle
measures.
1
4
2
65
7 8
3
14. Parallel Lines w/a transversal and
Angle Pair Relationships
Concept
Summary
Congruent Supplementary
alternate interior angles- AIA
alternate exterior angles- AEA
corresponding angles - CA
same side interior angles- SSI
Types of angle pairs formed when
a transversal cuts two parallel lines.
vertical angles- VA
linear pair of angles- LP
same side exterior angles- SSE
15. Now it’s Your turn!
• Name ALL angles congruent to ∠1.
s t
c
d
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
16. Name the pairs of the following angles formed by a
transversal.
Line M
BA
Line N
D E
P
Q
G
F
Line L
Line M
BA
Line N
D E
P
Q
G
F
Line L
Line M
BA
Line N
D E
P
Q
G
F
Line L
500
1300
17. REFERENCE CARD
• Learner’s Material – Mathematics VII, First Edition
2013 pp. 204- 207
• http://www.mathnstuff.com/math/spoken/here/2cla
ss/260/trans.htm
18. ANSWER CARD
Activity Card #1
1. X
2. O
3. O
4. O
5. X
Activity Card #2
1. ∠X, ∠Z, ∠D, ∠O
2. ∠W, ∠Y, ∠R, ∠A
3. ∠X and ∠O; ∠Z and ∠D
4. ∠W and ∠A; ∠Y and ∠R
5. ∠Wand ∠D; ∠X and ∠R; ∠Y and ∠O; ∠Z
and ∠A
6. ∠X and ∠D; ∠Z and ∠O
∠W and ∠R; ∠Y and ∠A
Activity Card #3
1. m∠Y=120°
2. m∠X=120°
3. m∠Z=60°
4. m∠D=60°
5. m∠0=120°
6. m∠R=60°
7. m∠A=120°
ASSESSMENT CARD
I.
1. corresponding angles
2. Alternate interior angles
3. Alternate exterior angles
4. Alternate interior angles
5. Alternate exterior angles
6. Corresponding angles
7. Same side exterior angle
8. Same side interior angle
9. Corresponding angles
10. Same side exterior angle
II.
m∠2=60°
m∠3=60°
m∠4=120°
m∠5=120°
m∠6=60°
m∠7=60°
ms∠8=120°
NOW IT’S YOUR TURN!
∠6; ∠3; ∠8; ∠9; ∠14; ∠11; ∠16
