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Alternate Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 30 of 59.

The four angles between the two parallels are the interior angles. Two interior angles on opposite sides of the transversal, one at each crossing, are alternate angles, and with parallel lines they are equal. Traced with the lines between them, they make a Z.

$Parallel lines and a transversal: alternate angles of 115 degrees between the lines, on opposite sides$

Why they match: take the angle at the top crossing. Its vertical angle is equal to it, and that vertical angle corresponds to the alternate angle at the bottom crossing. Two equal steps make one equal pair, so the rule Alternate angles skips the middle step.

The same works outside the parallels: the two outside angles on opposite sides are equal too. That pair has its own name in the menu, Alternate exterior angles.

Challenge

AB ∥ CD, cut by the transversal GH. Find the angle marked ?, 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 AnglesAlternate AnglesCo-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 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