3-3 Proving Lines Parallel

Quick Review

If two lines and a transversal form

• congruent corresponding angles,
• congruent alternate interior angles,
• congruent alternate exterior angles, or
• supplementary same-side interior angles, then the two lines are parallel.

Example

What is the value of x for which l || m ? l vertical linevertical line m question mark

The given angles are alternate interior angles. So, l || m l vertical linevertical line m  if the given angles are congruent.

Exercises

Find the value of x for which l || m . l vertical linevertical line m .

Use the given information to decide which lines, if any, are parallel. Justify your conclusion.

Image Long Description

18. ∠ 1 ≅ ∠ 9 angle 1 approximately equal to angle 9
19. m ∠ 3 + m ∠ 6 = 180 m angle , 3 plus , m angle , 6 equals 180
20. m ∠ 2 + m ∠ 3 = 180 m angle , 2 plus , m angle , 3 equals 180
21. ∠ 5 ≅ ∠ 11 angle 5 approximately equal to angle 11

3-4 Parallel and Perpendicular Lines

Quick Review

• Two lines || to the same line are || to each other.
• In a plane, two lines ⊥ to the same line are ||.
• In a plane, if one line is ⊥ to one of two || lines, then it is ⊥ to both || lines.

Example

What are the pairs of parallel and perpendicular lines in the diagram?

l || n , l || m , l vertical linevertical line n comma l vertical linevertical line m comma  and m || n . m vertical linevertical line n .

a ⊥ l , a ⊥ m , eh up tack l comma eh up tack m comma  and a ⊥ n . eh up tack n .

Exercises

Use the diagram below to complete each statement.

22. If b ⊥ c b up tack c  and b ⊥ d , b up tack d , comma  then c ? ¯ modified question mark with under bar below d.
23. If c || d , c vertical linevertical line d comma  then ? ¯ modified question mark with under bar below ⊥ c . up tack c .
24. Maps Morris Avenue intersects both 1st Street and 3rd Street at right angles. 3rd Street is parallel to 5th Street. How are 1st Street and 5th Street related? Explain.

Table of Contents