How To Solve Transversal Angles

In this critical geometry lesson, you'll larn all about parallel lines cutting by a transversal.

Jenn (B.S., M.Ed.) of Calcworkshop® introducing parallel lines cut by a transversal

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Y'all'll gain feel classifying line types, identifying angle relationships, and finally using that cognition to solve bug for missing angles.

Let jump in!

What Are Parallel Lines?

What comes to listen when yous think of parallel lines?

Is it the definition, which states that parallel lines are coplanar and never intersect because they are the same altitude apart?

Or perhaps you envision 2 lines that accept the same gradient and different y-intercepts as we learned in Algebra?

Or perhaps information technology's just a visual image like a railroad track or a scout fence.

parallel lines examples

Parallel Lines Examples

What Is A Transversal?

A transversal is a line that intersects two or more coplanar lines, each at a different point.

What this means is that, two lines are intersected by a tertiary line, and in and then doing, creates 6 angle-pair relationships as demonstrated below:

Interior angles: ∠3,∠iv,∠five,∠6
Exterior angles:∠1,∠ii,∠7,∠8
Pairs of alternate exterior angles: ∠1,∠7 ; ∠ii,∠8
Pairs of alternate interior angles: ∠iv,∠vi ; ∠iii,∠5
Pairs of corresponding angles: ∠1,∠5 ; ∠ii,∠6 ; ∠three,∠seven ; ∠4,∠eight
Paris of angles on the aforementioned-side of the transversal: ∠three,∠six ; ∠iv,∠5

transversal line example

Transversal Line Example

Parallel Lines and Transversals Postulates

Parallel lines and transversals are very important to the written report of geometry because they enable united states to define coinciding angle pair relationships.

How?

Well, when two parallel lines are cutting by a transversal (i.east., go crossed by a third line), then not merely practice we discover the vertical angles and linear pairs that are subsequently formed, simply the following bending pair relationships are created too:

Respective Angles are congruent
Alternating Outside Angles are congruent
Alternate Interior Angles are congruent
Same Side Interior Angles (Sequent Interior Angles) sum to 180 degrees

And knowing how to identify these angle pair relationships is crucial for proving 2 lines are parallel, as Study.Com accurately states.

In the video beneath, you lot'll discover that if 2 lines are parallel and are cut by a transversal, and so all pairs of corresponding angles are congruent (i.east., same measure), all pairs of alternate exterior angles are congruent, all pairs of alternating interior angles are coinciding, and same side interior angles are supplementary!

Transversal Angles

Corresponding Angles

∠1 is coinciding to ∠5
∠ii is congruent to ∠half dozen
∠3 is congruent to ∠7
∠4 is congruent to ∠viii

corresponding angles

Corresponding Angles

Alternating Exterior Angles

∠one is congruent to ∠8
∠2 is congruent to ∠7

alternate exterior angles

Alternate Outside Angles

Alternate Interior Angles

∠3 is coinciding to ∠5
∠4 is congruent to ∠half-dozen

alternate interior angles

Alternating Interior Angles

Same Side Interior Angles

∠three and ∠six are supplementary
∠4 and ∠five are supplementary

same side interior angles

Same Side Interior Angles

Wow!

In the following video, y'all'll learn all nigh classifying lines as parallel, intersecting, or skew. Then you'll learn how to identify transversal lines and angle pair relationships. Next, you'll utilize your noesis of parallel lines to decide the measure of angles. And lastly, yous'll write two-cavalcade proofs given parallel lines.

Parallel Lines Cut By A Transversal – Lesson & Examples (Video)

i hr 10 min

What are parallel, intersecting, and skew lines? (Examples #ane-eight)
00:09:34 – Overview of transversal and angle pair relationships (Examples #9-fourteen)
00:xx:52 – Theorems for perpendicular and parallel lines
00:28:47 – Detect the mensurate of each bending given two parallel lines cut by a transversal (Examples #15-xviii)
00:46:05 – Find the measure of each bending (Example #19)
Exclusive Content for Member'due south Only

00:49:49 – From the given information tin you prove the ii lines are parallel? (Example #20)
00:55:01 – Write a ii-column proof given parallel lines (Examples #21-23)
Practice Issues with Step-by-Footstep Solutions
Chapter Tests with Video Solutions