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  2. Base (geometry) - Wikipedia

    en.wikipedia.org/wiki/Base_(geometry)

    The extended base of a triangle (a particular case of an extended side) is the line that contains the base. When the triangle is obtuse and the base is chosen to be one of the sides adjacent to the obtuse angle, then the altitude dropped perpendicularly from the apex to the base intersects the extended base outside of the triangle. The area of ...

  3. Altitude (triangle) - Wikipedia

    en.wikipedia.org/wiki/Altitude_(triangle)

    The altitude from A (dashed line segment) intersects the extended base at D (a point outside the triangle). In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite the apex.

  4. Extended side - Wikipedia

    en.wikipedia.org/wiki/Extended_side

    In an obtuse triangle, the altitudes from the acute angled vertices intersect the corresponding extended base sides but not the base sides themselves.. The excircles of a triangle, as well as the triangle's inconics that are not inellipses, are externally tangent to one side and to the other two extended sides.

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    A triangle in which one of the angles is a right angle is a right triangle, a triangle in which all of its angles are less than that angle is an acute triangle, and a triangle in which one of it angles is greater than that angle is an obtuse triangle. [8] These definitions date back at least to Euclid. [9]

  6. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    The best known and simplest formula is = /, where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. Euclid proved that the area of a triangle is ...

  7. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

  8. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In a triangle, three intersection points, each of an external angle bisector with the opposite extended side, are collinear. [18]: 149 In a triangle, three intersection points, two between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended are collinear.

  9. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The Nagel triangle or extouch triangle of is denoted by the vertices , , and that are the three points where the excircles touch the reference and where is opposite of , etc. This T A T B T C {\displaystyle \triangle T_{A}T_{B}T_{C}} is also known as the extouch triangle of A B C {\displaystyle \triangle ABC} .