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Which Rule Is It

Part of the Angles section of Coddy's Geometry journey. Lesson 32 of 59.

Before any number, name the pair. Three questions sort every pair at two parallel crossings: Are both angles between the parallels? Are they on the same side of the transversal? Are they at the same crossing?

$Parallel lines and a transversal with four angles numbered 1 to 4$

In the figure, ∠1 and ∠2 are in the same position at the two crossings: corresponding, equal. ∠3 and ∠2 are both between the lines on opposite sides: alternate, equal. ∠3 and ∠4 are both between the lines on the same side: co-interior, adding to 180°. Two angles tip to tip at one crossing would be vertical angles.

Turn the figure or lean the transversal the other way, and the answers stay the same. The positions are what count, never which way the page is held.

Challenge

AB ∥ CD, cut by the transversal GH. The angles marked 1 and 2 are equal. Pick the rule that says why, then press Check.

Try it yourself

$Name the rule that links them$

Name the rule that links them

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 AnglesWhich Rule Is ItRecap: 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 Angles Perpendicular Lines Finding 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