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Height of an Isosceles

Part of the Triangles section of Coddy's Geometry journey. Lesson 51 of 60.

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.

$Isosceles triangle with equal sides 10, base 12 and height h to the midpoint D$

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

$Find the marked part of the figure$

Find the marked part of the figure

All lessons in Triangles

1The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side Recap: The Third Side

4Area of a Triangle

Half the Rectangle Height Is Not a Side Right Triangle Area Finding the Height Any Side Can Be the Base Recap: Area

7Is It Right?

The Converse Testing a Triangle Acute or Obtuse?Sorting by the Test Recap: Right or Not

10Scale in the World

Shadows Across the River Nested Triangles A Side with an Expression Recap: Scale in the World

2Sides and Names

Sorting by Sides The Longest Side Ticks into Equations Recap: Sorting Triangles

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an IsoscelesArea from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools