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Base Angles Are Equal

Part of the Angles section of Coddy's Geometry journey. Lesson 44 of 59.

A triangle with two equal sides is isosceles. The figure shows the equal sides with matching tick marks. The angles opposite those sides, the base angles, are equal. The third angle, between the two equal sides, is the apex.

$An isosceles triangle with two ticked sides, apex 40 degrees and base angles of 70 degrees$

Why they match: fold the triangle along the line from the apex to the middle of the base. The equal sides land on each other, so the two base angles land on each other too. Then the angle sum does the rest. With an apex of 40°, the two equal base angles share 180 - 40 = 140°, so each is 70°.

The rule on the board is Isosceles triangle. It knows both facts at once, equal base angles and the 180° total, so it finds a base angle from the apex in one step.

Challenge

Triangle ABC has two equal sides, marked with ticks. Its apex at C is 38°. Find the base angle at A, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

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 EqualFinding 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