# Ch 6: High School Geometry: Parallel Lines and Polygons

Watch video lessons and learn about parallel lines and the multi-sided figures known as polygons. These lessons utilize engaging animations and on-screen graphics to help you quickly retain critical info about polygons and parallel lines.

## Parallel Lines and Polygons - Chapter Summary and Learning Objectives

In this geometry chapter, instructors will help you learn about parallel lines, those straight objects on a plane that never intersect and are always the same distance away from each other. Using easy-to-understand explanations and drawings, the experienced instructors who lead these lessons will introduce you to the parallel postulate or hypothesis and the concept of indirect proof. You'll also learn about congruent angles, or those that are the same shape and size, as well as how to identify and measure angles and polygons. When you complete this chapter, you should be able to:

• Identify the angles formed by parallel lines and a transversal
• Use geometrical theories to prove that lines are parallel
• Indentify and measure the area, diagonal and perimeter of a polygon
• Measure the angles of polygons and triangles

VideoObjective
The Parallel Postulate and Indirect ProofDefine and provide examples of indirect proof, and explain how it relates to the parallel postulate.
Angles Formed by a TransversalDefine transversal. Identify angles formed by parallel lines and a transversal, and provide examples.
Parallel Lines: How to Prove Lines Are ParallelDiscuss how to prove lines are parallel, including those intersected by a transversal and pairs of congruent alternate exterior angles, congruent corresponding angles, congruent alternate exterior angles or supplementary interior angles on the same side of the transversal.
Using Converse Statements to Prove Lines Are ParallelApply the opposite of a statement to prove that: 1) When two parallel lines are intersected by a transversal, all pairs of alternate interior angles are congruent. 2) When two lines are parallel and a third line is perpendicular to one of them, it is also perpendicular to the other. 3) When two parallel lines are intersected by a transversal, all pairs of corresponding angles are congruent. 4) When two parallel lines are intersected by a transversal, all pairs of alternate exterior angles are congruent. 5) When two parallel lines are cut by a transversal, all pairs of interior angles on the same side of the transversal are supplementary.
What Are Polygons? - Definition and MeasurementsDefine a polygon, and describe how to measure its diagonal and perimeter. Determine properties and provide examples of a polygon's angles by constructing a line parallel to a given line that passes through a point not on the given line.
Measuring the Area of Regular PolygonsDescribe the apothem of a regular polygon. Explain how to apply the area formula, and provide examples.
Measuring the Angles of Triangles: 180 DegreesEstablish that the sum of angles of a triangle is 180°.
Measuring the Angles of a PolygonShow how to find the sum of measures of angles in a polygon.

12 Lessons in Chapter 6: High School Geometry: Parallel Lines and Polygons
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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