Display Title
Math Example--Solving Equations--Equations with Angles from Parallel Lines Cut by a Transversal--Example 8
Display Title
Equations with Angles from Parallel Lines Cut by a Transversal--Example 8
Topic
Equations
Description
This example continues the exploration of supplementary angles in parallel lines cut by a transversal, taking into account the property of corresponding angles. The diagram shows two parallel lines intersected by a transversal, with one alternate interior angle measuring 128° and the other labeled x°. The vertical angle to x is congruent and forms a pair of same side interior angles, which are supplementary. To solve for x, we simply set up the equation: x + 128 = 180. This example reinforces the consistent relationship between same side interior angles in parallel line configurations. It's important to note that this property is bidirectional - if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines must be parallel. This concept is often used in geometric proofs to establish the parallelism of lines. By working through multiple examples with different angle measures, students can internalize this fundamental property and apply it confidently in various geometric scenarios.
For a complete collection of math examples related to Equations of Parallel Lines click on this link: Math Examples: Equations of Parallel Lines Collection.
| Common Core Standards | CCSS.MATH.CONTENT.4.G.A.2, CCSS.MATH.CONTENT.8.G.A.5 |
|---|---|
| Grade Range | 4 - 8 |
| Curriculum Nodes |
Geometry • Points and Lines • Parallel Lines • Angles and Planes • Applications of Angles and Planes Algebra • Expressions, Equations, and Inequalities • Applications of Equations and Inequalities |
| Copyright Year | 2021 |
| Keywords | Parallel Lines Cut by a Transversal, parallel lines, transversal, vertical angles, supplementary angles, alternate interior angles, alternate exterior angles |
