Height of an Isosceles
Part of the Triangles section of Coddy's Geometry journey. Lesson 54 of 63.
The height from the apex of an isosceles triangle lands exactly on the middle of the base, and it cuts the triangle into two equal right triangles. Each has the leg of the isosceles triangle as its hypotenuse and half the base as one leg.
Here the equal sides are 10 and the base is 12. The ticks on BD and DC say D is the midpoint, so DC = 6. Then in the right triangle ADC, h^2 + 6^2 = 10^2, and h = 8. Two rules in a row: Midpoint, then Pythagorean theorem.
Challenge
△ABC is isosceles with AB = AC, and its height AD meets BC at the midpoint D. Find AD, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles11Two Tools at Once
Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg