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xGeometry

Isosceles Triangle

Base
$$b$$
Oblique Side
$$S$$
Height
$$h$$
$$2p = b + S \times 2$$
Perimeter
$$b = 2p - S \times 2$$
$$S = \frac{2p - b}{2}$$
$$A = \frac{b \times h}{2}$$
Area
$$b = \frac{A \times 2}{h}$$
$$h = \frac{A \times 2}{b}$$
$$S = \sqrt{ {h}^2 + {\left(\dfrac{b}{2}\right)}^2 }$$
Oblique Side (Pythagoras' theorem)
$$h = \sqrt{ {S}^2 - {\left(\dfrac{b}{2}\right)}^2 }$$
$$b = \sqrt{ {S}^2 - {h}^2 } \times 2$$
Definition
An isosceles triangle is a triangle with two congruent sides
Properties
  1. Two congruent sides
  2. Base angles are congruent
  3. All the  Generic Triangle formulas are valid
  4. The height relative to the base divides the shape in two congruent right triangles. For these are valid the  Right Triangle formulas