triangle and theormes

Scalene Triangle

A scalene triangle is a triangle that has three unequal sides,

Equiangular

An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60°

Third Angles Theorem

If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles is also congruent.

Converse of Isosceles Triangle Theorem

If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent. The converse of the base angles theorem, states that if two angles of a triangle are congruent, then sides opposite those angles are congruent.

Converse of Pythagorean Theorem

Image result for Converse of Pythagorean Theoremwww.onlinemathlearning.com The converse of the Pythagorean Theorem is also true. ... Pythagorean Theorem Converse: If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Triangle Midsegment Theorem

In a triangle, the segment joining the midpoints of any two sides will be parallel to the third side and half its length.

Isosceles Triangle

two equal sides. In

Obtuse Triangle

two of the interior angles are always acute (less than 90 degrees)*, so there are three possibilities for the third angle: Less than 90° - all three angles are acute and so the triangle is acute. Exactly 90° - it is a right triangle. Greater than 90° (obtuse): the triangle is an obtuse triangle.

Acute Triangle

with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle.

Legs of an Isosceles Triangle

In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

Base Angles of an Isosceles Triangles

In an isosceles triangle, the base angles have the same degree measure and are, as a result, equal (congruent). Similarly, if two angles of a triangle have equal measure, then the sides opposite those angles are the same length.

Triangle (Angle) Sum Theorem

The Angle Sum Theorem gives an important result about triangles, which is used in many algebra and geometry problems. We give the proof below. Theorem: The sum of the measures of the interior angles of a triangle is .

no name- If two angles of a triangle are not congruent, then the linger side is opposite the larger angle

The Hinge Theorem (SAS Inequality Theorem( If two sides of one triangle are congruent to two sides of another, and the included angles are not congruent then the longer third side is opposite the larger included angle.

Pythagorean Inequalities Theorem

The Pythagorean Inequality is a generalization of the Pythagorean Theorem, which states that in a right triangle with sides of length we have . This Inequality extends this to obtuse and acute triangles. The inequality says: For an acute triangle with sides of length , .

Legs of a Right Triangle

The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

no names- The acute angles of a right triangle are complementary

The acute angles of a right triangle are complementary. given: triangle ABC WITH RIGHT ANGLE C PROVE: ANGLE A AND ANGLE B are complementary. m(A) + m(B) = 90, hence they're complementary.

Centroid Theorem

The centroid of a triangle is the point where the three medians coincide. The centroid theorem states that the centroid is of the distance from each vertex to the midpoint of the opposite sid

Exterior Angle Theorem

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.

Hypotenuse

The longest side of a right triangle. The side opposite the right angle. In a right triangle (one where one interior angle is 90°), the longest side is called the hypotenuse. It is always the side opposite the 90° angle.

Incenter Theorem

The point where the three angle bisectors of a triangle meet. ... One of several centers the triangle can have, the incenter is the point where the angle bisectors intersect.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Circumcenter Theorem

The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter. Theorem: Circumcenter Theorem. The vertices of a triangle are equidistant from the

no name-f two sides of a triangle are not congruent, then the larger angle is opposite the longer side

Theorem If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. Theorem If two angles of a triangle are not congruent, then the longer side is opposite the larger angle.

Right Triangle

a triangle with a right angle. Also equals to 90 degrees

Interior Angle of a Triangle

can be 90° or more. In a right triangle, since one angle is always 90°, the other two must always add up to 90° A triangle is simply a polygon that has 3 sides. See interior angles of a polygon for the properties of the interior angles of a polygon with any number of sides

Side-Angle Inequality Theorem

here are two important theorems involving unequal sides and unequal angles in triangles. They are: Theorem 36: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.

Equilateral Triangle

in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Pythagorean Theorem

is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Base of an Isosceles Triangle

that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles.

Exterior Angle

the angle between a side of a rectilinear figure and an adjacent side extended outward.