Base Angles Are Equal
Part of the Angles section of Coddy's Geometry journey. Lesson 47 of 62.
A triangle with two equal sides is isosceles. The matching ticks mark the equal pair, and equality echoes into the corners: the two angles opposite the ticked sides, the base angles, are equal too.
Why equal? Fold the triangle along the line from the apex to the middle of the base: the two equal sides land on each other, so the two base corners land on each other too. In the figure the apex takes 40°, and the two equal base angles split the rest: 2y + 40 = 180, so 2y = 140 and y = 70. One unknown, counted twice, plus the apex: the triangle budget with a twist of symmetry.
Challenge
EasyThe triangle is isosceles with apex angle 50°; each base angle measures x°.
Find x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles
1Meet the Angle
Your First AngleNaming AnglesAdding Adjacent AnglesDegrees and the Full TurnAcute, Right, ObtuseRecap: Adjacent Angles4Vertical Angles
Linear PairsVertical Angles Are EqualSolving with VerticalsAll Four AnglesRecap: At the Crossing7Crossing Parallel Lines
Parallel LinesCorresponding AnglesAlternate AnglesCo-interior AnglesWhich Rule Is ItRecap: The Three Pairs10Isosceles Triangles
Base Angles Are EqualFinding the ApexWhich Angles MatchEquilateral AnglesIsosceles at WorkRecap: Twin Corners2Straight Lines and Supplements
Angles on a LineSupplementary AnglesThree Angles on a LineWrite the EquationRecap: Along the Line5Around a Point
Angles Around a PointThe Missing AngleEqual SlicesFour Angles, One PointRecap: The Full Turn3Right Angles and Complements
Complementary AnglesFinding the ComplementPerpendicular LinesEqual Parts of a CornerRecap: The Right Corner6The Angle Bisector
The Angle BisectorBisected ExpressionsBisecting a Straight AngleRecap: Split in Half