Based on the diagram below , which statement is true ?

1) a||b
2) b||c
3) a||c
4) d||e

Question

Based on the diagram below , which statement is true ?

1) a||b 
2) b||c
3) a||c
4) d||e

mathmale · Answer

Nina:  how about defining what you think the symbol || means?  How does one determine whether two lines (or line segments) are || or not?

anonymous · Answer

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mathmale · Answer

This is a VERY nice diagram.  
To help you determine whether two lines are parallel (||) or not, consider lines a and c.  Because line a is 110 degrees from the horizontal, measured clockwise, and line c is 115 degrees from the horizontal, they are NOT parallel.  However, if you were to change that 115 degrees to 110 degrees, then lines a and c would be parallel.  What further info might help you identify the correct answer to this problem?

mathstudent55 · Answer

To have parallel lines, corresponding angles must be congruent.

mathstudent55 · Answer

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mathstudent55 · Answer

In the figure above, lines a and b are cut by transversal line t.
The two angles formed by lines a and b and the transversal line t are called corresponding angles.
Since the two corresponding angles are congruent, you can conclude that lines a and b are parallel.

mathstudent55 · Answer

Now look in your figure. Fill in the measures of other angles. See if you find any two angles of the same measure.

mathstudent55 · Answer

These two angles are not congruent, so lines a and c are not parallel.
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