Question

Use the diagram below in the following exercise.
How would you show that the lines b and c are parallel?
e
bo
g
d
\1 240
a
1299
1290
132
519
560
b
519
t
A
Use the Alternate Exterior Angles Converse Theorem.
B
Use the Corresponding Angles Converse Postulate.
Use the Consecutive Interior Angles Converse Theorem.
Use the Alternate Interior Angles Converse Theorem.

Answer 1

The way to show that lines b and c are parallel in the diagram given is to apply the: B. Corresponding Angles Converse Postulate

Note the following:

• From the diagram given, parallel lines b and c are cut across by transversal g.
• One of the angles formed at the point of intersection of line b and transversal g is 51 degrees.
• Another angle formed at the intersection of line c and transversal g is also 51 degrees.

Thus:

Both angles lie in corresponding positions to each other. Both angles are corresponding angles.

Since both angles are corresponding angles that are congruent, lines b and c are therefore parallel lines based on the Converse of the Postulate of Corresponding Angles.

Therefore, a way to show that lines b and c are parallel in the diagram given is to apply the: B. Corresponding Angles Converse Postulate

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