### 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.

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 $$x$$.

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 $$x$$.

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

$$12x + 3 = 11x + 9$$

$$x = 6$$

21554 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:

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16943 x

Solve for x.

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

Example of one question:

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11275 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:

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### Geometry

Circles
Congruent Triangles
Constructions
Parallel Lines and the Coordinate Plane
Properties of Triangles

### Algebra and Pre-Algebra

Beginning Algebra
Beginning Trigonometry
Equations
Exponents
Factoring
Linear Equations and Inequalities
Percents
Polynomials
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