Triangle#Types of triangle

An isosceles triangle is a triangle with two equal sides. Consequently, the two angles are of equal size, which are opposite the sides of equal length. For the complete determination of two determining factors are required, of which at least one page.

The two equal sides are called legs, the third side is called the base. The base of the opposite vertex is called top. The voltage applied to the base angles are called base angles.

Each isosceles triangle is axisymmetric. It may be acute-angled, right-angled or obtuse.

Calculation and design

Formulas of the isosceles triangle

Base angle theorem

The base angle theorem states that the two base angles, ie the angles which are equal length sides opposite are equal in size in an equilateral triangle. The opposite also holds: If two angles in a triangle equal, the two opposite sides are of equal length.

In the literature, the basic angle set under the name mnemonic (Latin pons Asinorum ).

Two sides

In the isosceles triangle is formed by two different long sides at once, the third co-determined if you know which of the sites is the basis. This results in an SSS case. The angle can be calculated using the cosine law.

One side and one angle

If an angle is given, can be derived from the relationship

Immediately compute all remaining angles. This allows you to treat the triangle to the WSW- case. The missing pages can be calculated using the law of sines.

Excellent points

Isosceles triangles are axisymmetric. The axis of symmetry coincides with the height of the perpendicular bisector ( bisector ) and the median line ( focal line) of the base and with the bisector ( angle bisector ) of the angle at the top. The orthocenter, the circumcenter, the center of gravity and the incenter lie on this axis of symmetry.

In an isosceles triangle that is not equilateral, right Euler's Just So in line with the axis of symmetry.

• Axis of symmetry
• Midperpendicular and circumcenter
• Seitenhalbierende and focus
• Bisector and incenter

See also: Excellent points in the triangle