A triangle with exactly 2 congruent sides. There are many interesting facts about this kind of triangle, such as:

• The angle bisector of the vertex angle (the top one) is the perpendicular bisector of the base.
• The non-vertex angles are congruent.
• If the vertex angle measures 90 degrees, then if the base measures x, the hypotenuse measures sqrt(2)x.

An isosceles triangle is a triangle with at least two congruent sides; that is to say, at least two sides are exactly the same length. This will mean that it also has two congruent (identical) angles, and it is bilaterally symmetrical.

An equilateral triangle is a special case of the isosceles triangle, in which all three sides are the same length, and all of its internal angles are also the same, 60°. These are in contrast to scalene triangles, in which all sides are different lengths.

When only two sides are equal, it is traditional to refer to the unequal side as the base of the triangle. This puts the odd angle out at the top, making it the vertex angle. The vertex will be centered directly over the midpoint of the base.

The right isosceles triangle (AKA the 45-45-90 triangle) is one of the most commonly seen triangles, and is used widely in architecture and engineering. It has one right angle (90°), and two 45° angles. This is the only right triangle that is also an isosceles triangle.

Isosceles comes from the Greek word isoskeles, itself a compound word, from iso, meaning 'same', and skelos, meaning 'leg'. It is pronounced eye-sos-uh-lees.

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