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Perpendicular Lines

Part of the Angles section of Coddy's Geometry journey. Lesson 10 of 59.

Two lines are perpendicular when they cross at a right angle. The sign is ⊥: AC ⊥ DE says the line AC is perpendicular to the line DE.

$Two perpendicular lines AC and DE crossing at B, one corner marked with a square$

One right angle at a crossing makes all four right. In the figure only ∠CBE carries the square. Its neighbour ∠EBA sits with it on the straight line AC, so ∠EBA is 180 - 90, another 90°. The same works all the way round, so a figure needs only one square, or the words AC ⊥ DE, to mark every corner.

So treat each of the four corners as a marked right angle. If a ray splits one of them into 40° and 50°, those parts are complementary, exactly as in the last lesson.

Challenge

The lines AC and DE are perpendicular: AC ⊥ DE. The ray BF lies inside the corner ABD. Find ∠FBD, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

All lessons in Angles

1Meet the Angle

Your First Angle Angles on a Line Degrees and the Full Turn Across the Crossing

4Vertical Angles

Two Lines Cross Vertical Angles Are Equal Solving with Verticals All Four Angles Recap: At the Crossing

7Parallels and Transversals

Parallel Lines Corresponding Angles Alternate Angles Co-interior Angles Which Rule Is It Recap: The Three Pairs

10Isosceles and Equilateral

Base Angles Are Equal Finding the Apex Which Angles Match Equilateral Angles Isosceles at Work Recap: Twin Corners

2Naming and Equations

Adding Adjacent Angles Write the Equation Recap: Along the Line

5Around a Point

Angles Around a Point The Missing Angle Equal Slices Four Angles, One Point Recap: The Full Turn

8Angle Chases

Verticals Meet Parallels Is There Enough?From Figure to Equation Both Angles Labeled Recap: Through the Strip

11The Exterior Angle

The Exterior Angle Using the Shortcut Two Roads, One Answer Exterior in the Wild Recap: Outside View

3Right Angles and Complements

The Square Mark Complementary AnglesPerpendicular LinesFinding the Complement Equal Parts of a Corner Recap: The Right Corner

6The Angle Bisector

The Angle Bisector Bisected Expressions Bisecting a Straight Angle Recap: Split in Half

9Triangle Angle Sum

The 180 Rule Finding the Third Angle Two Unknown Angles Right Triangles Recap: The Budget

12Final Challenges

Final: The Angle Chase Final: Triangle Meets Line Final: The Full Round Final: Isosceles Chase Final: Master of Angles