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The 180 Rule

Part of the Angles section of Coddy's Geometry journey. Lesson 39 of 59.

The three angles inside any triangle add up to 180°. Tall or flat, wide or thin, the total never changes, and the parallel lines from the last chapters show why.

$A triangle ABC with a line through C parallel to AB; matching arcs show the base angles copied up to C$

Draw a line through the top corner C, parallel to the base AB. The angle at A has an alternate twin at C, between CA and the new line (one arc each). The angle at B has one on the other side (two arcs each). At C the two twins and the triangle's own angle at C (three arcs) sit side by side on the straight line, so they add up to 180°. The twins equal the angles at A and B, so the triangle's three angles add up to 180° too.

On the board this rule is Angles in a triangle. A triangle is three points, not on one line, joined by three drawn sides.

Challenge

Drag the corner C anywhere you like and watch the three angles of the triangle change. Keep an eye on their total, then press Check.

Try it yourself

$Drag the figure and watch$

Drag the figure and watch

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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 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 RuleFinding 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