All SSAT Upper Level Math Resources
Example Questions
Example Question #1 :Properties Of Parallel And Perpendicular Lines
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?
Line Q
Line S
Line P
Line R
None of the other responses is correct.
Line S
First, find the slope of the line of the equationby 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 #2 :Properties Of Parallel And Perpendicular Lines
You are given three lines as follows:
Line A includes pointsand.
Line B includes pointand has-intercept.
Line C includes the origin and point.
这行re parallel?
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 #1 :Properties Of Parallel And Perpendicular Lines
Line A has equation.
Line B has equation.
Which statement is true of the two lines?
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 #1 :Properties Of Parallel And Perpendicular Lines
Figure NOT drawn to scale
In the above figure,. Evaluate.
Angles of degree measuresandform a linear pair, making the angles supplementary - that is, their degree measures total 180. Therefore,
Solving for:
The angles of measuresandform 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 #5 :Properties Of Parallel And Perpendicular Lines
Figure NOT drawn to scale
In the above figure,. Expressin terms of.
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 forby moving the other terms to the other side and simplifying:
Example Question #421 :Geometry
Figure NOT drawn to scale
In the above figure,. Expressin terms of.
The two marked angles are corresponding angles of two parallel lines formed by a transversal, so the angles are congruent. Therefore,
Solving forby subtracting 28 from both sides:
Example Question #7 :Properties Of Parallel And Perpendicular Lines
Figure NOT drawn to scale
In the above figure,. Evaluate.
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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