Perpendicular Lines - Varsity Tutors

Home » What Does Perpendicular Look Like » Perpendicular Lines - Varsity Tutors

Maybe your like

Skip to main contentVarsity Tutors LogoHotMathPerpendicular Lines

Perpendicular Lines

Study Guide

Key Definition

Perpendicular lines are lines, segments, or rays that intersect to form right angles. The symbol $\perp$ means is perpendicular to.

Important Notes

  • If two lines are perpendicular, they form a $90^\circ$ angle.
  • In three dimensions, lines can be mutually perpendicular.
  • Let O be the intersection point of lines AB and CD.
  • $AB \perp CD$ means $\angle B O D = 90^\circ$.
  • The right angle symbol indicates perpendicularity.
  • Perpendicular lines are fundamental in geometry.

Mathematical Notation

$\perp$ means is perpendicular to$\angle$ represents an angleRemember to use proper notation when solving problems

Why It Works

Perpendicular lines form right angles of $90^\circ$. By definition, these right angles partition the plane into four congruent quadrants, illustrating how perpendicularity ensures equal angular spacing.

Remember

Perpendicular lines always intersect at $90^\circ$ angles.

Quick Reference

Right Angle:$90^\circ$

Understanding Perpendicular Lines

Choose your learning level

Watch & Learn

Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Perpendicular lines form a $90^\circ$ angle with each other. When two lines intersect at this angle, they are perpendicular.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Let O be the intersection of lines AB and CD. If $AB \perp CD$, what is $\angle B O D$?

A$90^\circ$B$60^\circ$C$45^\circ$D$120^\circ$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Real-world Scenario

Imagine you are designing a skateboard ramp that needs to be perpendicular to the ground. How would you ensure the ramp forms a $90^\circ$ angle with the ground?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider two streets that need to be perpendicular for proper traffic flow. How would you verify the streets form a $90^\circ$ angle?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Let O be the intersection of lines AB and CD. Which of the following is true for lines $AB$ and $CD$ if $AB \perp CD$?

A$\angle A O C = 90^\circ$B$\angle A O C = 45^\circ$C$\angle A O C = 60^\circ$D$\angle A O C = 180^\circ$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

Watch & Learn

Review key concepts and takeaways

recap. Use space or enter to play video.recap thumbnail

Tag » What Does Perpendicular Look Like