Download Reteach 3-3 - Dragonometry

Name
LESSON
3-3
Date
Class
Reteach
Proving Lines Parallel
Converse of the Corresponding
Angles Postulate
You can use the Converse of the
Corresponding Angles Postulate
to show that two lines are parallel.
If two coplanar lines are cut by a transversal
so that a pair of corresponding angles are
congruent, then the two lines are parallel.
1 2
Q
34
R
Given: /1 > /3
/1 > /3
q || r
/1 > /3 are corresponding angles.
Converse of the Corresponding Angles Postulate
Given: m/2 5 3x°, m/4 5 (x 1 50)°, x 5 25
m/2 5 3(25)° 5 75°
Substitute 25 for x.
m/4 5 (25 1 50)° 5 75° Substitute 25 for x.
m/2 5 m/4
Transitive Property of Equality
/2 > /4
Definition of congruent angles
q || r
Converse of the Corresponding Angles Postulate
For Exercises 1 and 2, use the Converse of the Corresponding
Angles Postulate and the given information to show that c || d.
1. Given: /2 > /4
/2 > /4
c || d
/2 and /4 are corr. ?.
Conv. of Corr. ? Post.
1
3
2
4
C
D
2. Given: m/1 5 2x°, m/3 5 (3x 2 31)°, x 5 31
m/1 5 2x°
5 2(31)° 5 62°
m/3 5 (3x 2 31)°
5 3(31)° 2 31° 5 62°
m/1 5 m/3
/1 > /3
c || d
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Substitute 31 for x.
Substitute 31 for x.
Trans. Prop. of 5
Def. of > ?
Conv. of Corr. ? Post.
22
Holt Geometry
Name
LESSON
3-3
Date
Class
Reteach
Proving Lines Parallel continued
You can also prove that two lines are parallel by using the converse of any of
the other theorems that you learned in Lesson 3-2.
Theorem
Hypothesis
Conclusion
T
A
2
Converse of the Alternate
Interior Angles Theorem
3
B
a || b
/2 > /3
T
1
F
Converse of the Alternate
Exterior Angles Theorem
4
G
f || g
/1 > /4
S
1
Converse of the Same-Side
Interior Angles Theorem
2
T
s || t
m/1 1 m/2 5 180°
For Exercises 3–5, use the theorems and the given information to
show that j i k.
3. Given: /4 > /5
/4 > /5
jik
/4 and /5 are alt. int. ?.
Conv. of Alt. Int. ? Thm.
12
3 4
5 6
78
J
K
4. Given: m/3 5 12x°, m/5 5 18x°, x 5 6
m/3 5 12(6)° 5 72°
m/5 5 18(6)° 5 108°
m/3 1 m/5 5 72° 1 108° 5 180°
jik
Substitute 6 for x.
Substitute 6 for x.
Add angle measures.
Conv. of Same-Side Int. ? Thm.
5. Given: m/2 5 8x°, m/7 5 (7x 1 9)°, x 5 9
m/2 5 8(9)° 5 72°
m/7 5 7(9)° 1 9° 5 72°
m/2 5 m/7
/2 > /7
jik
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Substitute 9 for x.
Substitute 9 for x.
Trans. Prop. of 5
Def. of > ?
Conv. of Alt. Ext. ? Thm.
23
Holt Geometry