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Theorem: Bisector of Vertical Angle of an Isosceles Triangle Bisects the Base.

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In an isosceles triangle, two sides are equal in length. An isosceles triangle also has two angles of the same measure (Our solved example in mathguru.com uses this concept); namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem. Some mathematicians define an isosceles triangle to have exactly two equal sides, whereas others define an isosceles triangle as one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles.

A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). (Our solved example in mathguru.com uses this concept)

The side opposite to the right angle is the hypotenuse; it is the longest side of the right triangle.




Congruence (geometry)


In geometry, two figures are congruent if they have the same shape and size. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections.

The related concept of similarity permits a change in size.


Congruence of triangles


Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as:

In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two triangles.


SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. (Our solved example in mathguru.com uses this concept)




Supplementary angles


Supplementary angles are pairs of angles that add up to 180 degrees. (Our solved example in mathguru.com uses this concept)

If the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a line. The supplement of an angle of 135 degrees is an angle of 45 degrees. The supplement of an angle of x degrees is an angle of (180 − x) degrees. Supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary.




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.