SSAT Upper Level Math : How to find whether lines are parallel

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : How To Find Whether Lines Are Parallel

Line P passes through the origin and point .

Line Q passes through the origin and point .

Line R passes through the origin and point .

Line S passes through the origin and point .

Which of these lines is parallel to the line of the equation  ?

 

Possible Answers:

Line P

None of the other responses is correct.

Line S

Line Q

Line R

Correct answer:

Line S

Explanation:

First, find the slope of the line of the equation  by rewriting it in slope-intercept form:

The slope of this line is , so we are looking for a line which also has this slope.

Find the slopes of all four lines by using the slope formula . Since each line passes through the origin, this formula can be simplified to

using the other point.

 

 

Line P:

Line Q:

Line R: 

Line S:

Line S has the desired slope and is the correct choice.

 

Example Question #1 : How To Find Whether Lines Are Parallel

You are given three lines as follows:

Line A includes points  and .

Line B includes point  and has -intercept .

Line C includes the origin and point .

Which lines are parallel?

Possible Answers:

Correct answer:

Explanation:

Find the slope of all three lines using the slope formula :

Line A:

 

Line B:

 

Line C: 

 

Lines A and C have the same slope; Line B has a different slope. Only Lines A and C are parallel.

Example Question #2 : How To Find Whether Lines Are Parallel

Line A has equation .

Line B has equation .

Which statement is true of the two lines?

Possible Answers:

Correct answer:

Explanation:

Write each statement in slope-intercept form:

 

Line A:

The slope is .

 

Line B:

The slope is .

 

The lines have differing slopes, so they are neither identical nor parallel. The product of the slopes is , so they are not perpendicular. The correct response is that they are distinct lines that are neither parallel nor perpendicular.

Example Question #3 : How To Find Whether Lines Are Parallel

Parallel

Figure NOT drawn to scale

In the above figure, . Evaluate .

Possible Answers:

Correct answer:

Explanation:

Angles of degree measures  and  form a linear pair, making the angles supplementary - that is, their degree measures total 180. Therefore,

Solving for :

The angles of measures  and  form a pair of alternating interior angles of parallel lines, so, as a consequence of the Parallel Postulate, they are congruent, and

Substituting for :

Example Question #4 : How To Find Whether Lines Are Parallel

Parallel

Figure NOT drawn to scale

In the above figure, . Express  in terms of .

Possible Answers:

Correct answer:

Explanation:

The two marked angles are same-side interior angles of two parallel lines  formed by a transversal ; by the Parallel Postulate, the angles are supplementary - the sum of their measures is 180 degrees. Therefore,

Solve for  by moving the other terms to the other side and simplifying:

Example Question #5 : How To Find Whether Lines Are Parallel

Parallel

Figure NOT drawn to scale

In the above figure, . Express  in terms of .

Possible Answers:

Correct answer:

Explanation:

The two marked angles are corresponding angles of two parallel lines formed by a transversal, so the angles are congruent. Therefore,

Solving for  by subtracting 28 from both sides:

Example Question #7 : How To Find Whether Lines Are Parallel

Parallel

Figure NOT drawn to scale

In the above figure, . Evaluate .

Possible Answers:

Correct answer:

Explanation:

The two marked angles are same-side exterior angles of two parallel lines formed by a transversal ,; by the Parallel Postulate, the angles are supplementary - the sum of their measures is 180 degrees. Therefore,

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