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Any two pairs of angles are congruent, [4] which in Euclidean geometry implies that all three angles are congruent: [a] If ∠BAC is equal in measure to ∠B'A'C', and ∠ABC is equal in measure to ∠A'B'C', then this implies that ∠ACB is equal in measure to ∠A'C'B' and the triangles are similar. All the corresponding sides are ...
All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. This is a total of six equalities, but three are often sufficient to prove congruence ...
SSS (side-side-side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent. ASA (angle-side-angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. The ASA postulate is attributed to Thales of Miletus.
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon . Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint.
Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need to be a convex polygon: it could be concave or even self-intersecting.
Primitive Heronian triangle; Right triangle. 30-60-90 triangle; Isosceles right triangle; Kepler triangle; Scalene triangle; Quadrilateral – 4 sides Cyclic quadrilateral; Kite. Rectangle; Rhomboid; Rhombus; Square (regular quadrilateral) Tangential quadrilateral; Trapezoid. Isosceles trapezoid; Trapezus; Pentagon – 5 sides; Hexagon – 6 ...
Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...