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This essential trains for: SAT-I, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

Triangles are polygons with three angles (and three sides).

Sum of angles: The sum of the angles of a triangle is 180°.

Consequence: Only one angle of a triangle may be obtuse.

Triangle inequality: For three segments to form a triangle, any two of them must have a combined length that exceeds the length of the third one.

Isosceles triangle:

- has two sides of equal length (are congruent);
- the two angles adjacent to these sides have the same measure (are congruent);
- has a line of symmetry;

The line of symmetry of an isosceles triangle is also:

- altitude;
- angle bisector;
- median;
- perpendicular bisector;

Equilateral triangle:

- has three sides of equal length (are congruent);
- has three angles that have the same measure (are congruent);
- has three lines of symmetry;

The lines of symmetry of an equilateral triangle are also:

- altitudes;
- angle bisectors;
- medians;
- perpendicular bisectors;

Note: The plane may be tiled with equilateral triangles.

A right-angle triangle: is half of a rectangle.