Types of triangles based on sides

By Angle • Right Triangle: It has one angle equal to 90 degrees. The other two are acute angles, i.e. they measure less than 90 degrees. • Oblique Triangle: It hasn’t any angle measuring 90 degrees. Oblique triangles can be classificated in: • Acute Triangle: all three angles are acute, that is, its angles measure less than 90°. • Obtuse Triangle: One of its angles is greater than 90°. The other two are acute (less than 90°).

Identifying Scalene, Isosceles, and Equilateral Triangles - dummies The following are triangle classifications based on sides: • Scalene triangle: A triangle with no congruent sides • Isosceles triangle: A triangle with at least two congruent sides • Equilateral triangle: A triangle with three congruent sides (For the three types of triangles based on the measure of their angles, see the article, “Identifying Triangles by Their Angles.”) Because an equilateral triangle is also isosceles, all triangles are either scalene or isosceles. But when people call a triangle isosceles, they’re usually referring to a triangle with only two equal sides, because if the triangle had three equal sides, they’d call it equilateral. So does this classification scheme involve three types of triangles or only two? You be the judge. Identifying scalene triangles In addition to having three unequal sides, scalene triangles have three unequal angles. The shortest side is across from the smallest angle, the medium side is across from the medium angle, and — surprise, surprise — the longest side is across from the largest angle. The above figure shows an example of a scalene triangle. The ratio of sides doesn’t equal the ratio of angles. Don’t assume that if one side of a triangle is, say, twice as long as another side that the angles opposite those sides are also in a 2 : 1 ratio. The ratio of the sides may be close to the ratio of the angles, but these ratios are never exactly equal (except whe...

Parts of a Triangle A triangle has nine parts or elements, namely three sides, three angles and three vertices. If \(P, Q, R\) are three non-collinear points on the plane of the paper, then the figure made up by the three-line segments \(PQ, QR\) and \(RP\) is called a triangle with vertices \(P, Q \) and \(R\). The triangle with vertices \(P, Q\) and \(R\) is generally denoted by the symbol \(\Delta PQR\). Note that the triangle \(\Delta PQR\) consists of all the points on the line segments \(PQ, QR\) and \(RP\). Sides: The three-line segments \(PQ, QR\) and \(RP\), that form the triangle \(\Delta PQR\) are called the sides of the triangle \(\Delta PQR\). Angles: The three angles \(\angle QPR,\,\angle PQR\) and \(\angle PRQ\) are called the angles of \(\Delta PQR\). For the sake of convenience, we shall denote angles \(\angle QPR,\angle PQR\) and \(\Delta PQR\) by angles \(\angle P,\,\angle Q\) and \(\angle R,\) respectively. Vertices: The vertex is the point in a triangle where the two sides meet. In the \(\Delta PQR\), the points \(P, Q\) and \(R\) are the vertices. Elements or parts: The three sides \(PQ, QR, RP,\) angles \(\angle P,\,\angle Q,\,\angle R\) of a triangle \(PQR\) are together called the six parts or elements of the triangle \(PQR\). Classification of Triangles Triangles are classified based on \((a)\) the length of sides \((b)\) based on the measure of the angles. Classification of Triangles based on the Length of Sides Scalene Triangle A triangle having...