Up

Parallel lines and transversals

When two parallel lines are “cut” by a transversal, some special properties arise.  We will begin by stating these properties, and then we can use these properties to solve some problems.

PROPERTY 1:  When two parallel lines are cut by a transversal, then corresponding angles are congruent.

In the diagram below, angles 1 and 5 are corresponding, and so they are equal.  Similarly with angles 4 and 8, etc.

Parallel-Lines-Transversals-1

PROPERTY 2:  When two parallel lines are cut by a transversal, then adjacent angles are supplementary.  That is, when two parallel lines are cut by a transversal, then the sum of adjacent angles is \(180^\circ \).

In the diagram above, this property tells us that angles 1 and 2 sum to \(180^\circ \).  Similarly with angles 5 and 6.

EXAMPLE:  Solve for \(x\).

Parallel-Lines-Transversals-2

SOLUTION:  From property 2, we know that the 2 angles \(x + 75\), and \(A\) (so called by me) are supplementary.  That is,

\(x + 75 + A = 180\)

But from property 1, we know that \(A = x + 125\), since those two angles are corresponding.  Then \(x + 75 + x + 125 = 180\), so that \(2x + 200 = 180\). Then \(2x =  - 20\), and \(x =  - 10\).

EXAMPLE:  Solve for \(x\).

Parallel-Lines-Transversals-3

SOLUTION:  Since, by property 1, we know that corresponding angles are congruent, we know that

\(12x + 3 = 11x + 9\)

\(x = 6\)

Below you can download some free math worksheets and practice.


Downloads:
21353 x

Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Parallel-Lines-and-the-Coordinate-Plane-Parallel-lines-and-transversals-Easy

Watch below how to solve this example:

 

Downloads:
16756 x

Solve for x.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Parallel-Lines-and-the-Coordinate-Plane-Parallel-lines-and-transversals-Medium

Watch below how to solve this example:

 

Downloads:
11161 x

Find the measure of the angle indicated in bold.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Parallel-Lines-and-the-Coordinate-Plane-Parallel-lines-and-transversals-Hard

Watch below how to solve this example:

 
 
 

Facebook PageYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems