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  2. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.

  3. File:45° 45° 90° Special Right Triangle.svg - Wikipedia

    en.wikipedia.org/wiki/File:45°_45°_90°_Special...

    English: This file illustrates the special right triangle of angles 45°, 45° and 90°. Inside, the triangle is depicted with all of its angles and side lengths. The right angle is marked as a small square. To the right of the 90° angle is another angle represented by an arc, and its measure, 45°, is written to the left of it. Atop the right ...

  4. File:45-45-triangle.svg - Wikipedia

    en.wikipedia.org/wiki/File:45-45-triangle.svg

    Diagram demonstrating the ratios of the sides of a 45-45-90 special right triangle. ... the ratios of the sides of a 30-60-90 special right triangle. Created in ...

  5. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:

  6. Right triangle - Wikipedia

    en.wikipedia.org/wiki/Right_triangle

    A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).

  7. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Sines and cosines of common angles 0°, 30°, 45°, 60° and 90° follow the pattern ... Image mnemonic to help remember the ratios of sides of a right triangle.

  8. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.

  9. Ailles rectangle - Wikipedia

    en.wikipedia.org/wiki/Ailles_rectangle

    Drawing a line connecting the original triangles' top corners creates a 45°–45°–90° triangle between the two, with sides of lengths 2, 2, and (by the Pythagorean theorem) . The remaining space at the top of the rectangle is a right triangle with acute angles of 15° and 75° and sides of 3 − 1 {\displaystyle {\sqrt {3}}-1} , 3 + 1 ...

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