Examples of the squeeze theorem, g(x) ? f(x) ? h(x), show that if f(x) is always greater than g(x) and if f(x) is always less than h(x), then when g(x) is equal to h(x), f(x) must also be equal. Since f(x) always squeezes between g(x) and h(x), it must be equal when g(x) and h(x) are equal.
The angle bisector theorem states that a line bisecting an angle in a triangle divides the side opposite the angle into two line segments that have lengths proportional to the lengths of the other sides. An angle bisector is a line that divides an angle into two equal angles; it is often depicted as
The parallel axis theorem states that the "moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space," according to HyperPhysics. It is also know as Steiner's theorem.
The exterior angle theorem states that an angle exterior to a triangle equals the sum of the two angles not adjacent to it. The theorem’s basis derives from the fact that the sum of all the interior angles in a triangle equals 180 degrees.
The perpendicular bisector theorem is applicable for line segments. The theorem states that the perpendicular bisector is a line that represents the locus of points that are equidistant from the endpoints of the line segment that it intersects.
The Pythagorean theorem forms the basis of trigonometry and, when applied to arithmetic, it connects the fields of algebra and geometry, according to Mathematica.ludibunda.ch. It has been applied to real-world problems since at least 1500 B.C., when it was used by the ancient Babylonians to accurate
The same-side interior angles theorem states that two same-side interior angles are supplementary when two parallel lines are intersected by the transverse line. Same-side interior angles are two angles that are on the same side of the transverse line and on the interior of the two parallel lines. T
Four different methods for determining triangle congruency by examining sets of sides and angles exist: SSS (side, side, side), SAS (side, angle, side), ASA (angle, side, angle) and AAS (angle, angle, side). The hypotenuse and leg method can also determine the congruency of right triangles.
The Pythagorean Theorem can be used in any real life scenario that involves a right triangle having two sides with known lengths. In a scenario where a certain section of a wall needs to be painted, the Pythagorean Theorem can be used to calculate the length of the ladder needed if the height of the
The corollary to the triangle sum theorem is the law of cosines, better known as the Pythagorean theorem. This theorem is often used in calculus courses.