Can you have an obtuse equilateral triangle

Updated February 11, Infoplease Staff. Numbers and Formulas. See also:. Geometry: A Formal Introduction. Trending Here are the facts and trivia that people are buzzing about. Is Vatican City a Country? The Languages of Africa. The Mongol Empire.

The Most and Least Religious Countries. Property 1: The longest side of a triangle is the side opposite to the obtuse angle. See the image below for reference. Property 2: A triangle can only have one obtuse angle. Consider the obtuse triangle shown below. Hence, a triangle cannot have two obtuse angles because the sum of all the angles cannot exceed degrees. Observe the image given below to understand the same with an illustration.

Property 4: The circumcenter and the orthocenter of an obtuse-angled triangle lie outside the triangle. The orthocenter O , the point at which all the altitudes of a triangle intersect, lies outside in an obtuse triangle.

As seen in the image below:. Circumcenter H , the median point from all the triangle vertices, lies outside in an obtuse triangle. Example 1: Which of the following angle measures can form an obtuse-angled triangle? Among the given options, option b satisfies the condition. Therefore, option b i.

Therefore, the height of the obtuse triangle can be calculated by:. Example 3: Can sides measuring 3 inches, 4 inches, and 6 inches form an obtuse triangle? The sides of an obtuse triangle should satisfy the condition that the sum of the squares of any two sides is lesser than the square of the third side. The given measures can form the sides of an obtuse triangle. Therefore, 3 inches, 4 inches, and 6 inches can be the sides of an obtuse triangle.

It has one of its vertex angles as obtuse and other angles as acute angles i. An obtuse triangle can also be called an obtuse-angled triangle. Note: It is possible for an acute triangle to also be scalene, isosceles, or equilateral. A right triangle has one right angle. A "box" is used to indicate the location of the right angle. The longest side of the right triangle across from the "box" is called the "hypotenuse". The remaining two sides are referred to as "legs", which may, or may not, be of equal length.

Note: It is possible for a right triangle to also be scalene or isosceles. It is not possible to draw a triangle with more than one obtuse angle. Note: It is possible for an obtuse triangle to also be scalene or isosceles. An equiangular triangle has three congruent angles.