Are All Obtuse Triangles Similar

A triangle is a airtight two-dimensional airplane figure with 3 sides and three angles. Based on the sides and the interior angles of a triangle, different types of triangles are obtained and the birdbrained-angled triangle is one among them. If i of the interior angles of the triangle is obtuse (i.e. more than 90°), so the triangle is chosen the birdbrained-angled triangle.

The obtuse angle in the triangle tin can be any i of the three angles and the remaining two angles are acute. This triangle is also said every bit anobtuse triangle. Acute and right triangles are the other two triangles apart from obtuse, which are based on the angles. Just astute and obtuse are the all-time examples of a scalene triangle.

Table of contents:

Definition
Obtuse Angle
Formula
Determining Birdbrained Triangle
Properties
Case

Obtuse Angled Triangle Definition

A triangle whose whatever i of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle. The sum of the interior angles of the obtuse triangle is equal to 180° only. This means the bending sum property for whatsoever triangle remains the same.

Thus, if one angle is obtuse or more than ninety°, then the other two angles are definitely acute or both the angles are less than ninety°.

Obtuse Angled Triangle

The obtuse angle triangle properties are unlike from other triangles. Look at the tabular array below for the same:

Triangle type	Obtuse	Astute	Right
Departure	Any One bending more than xc°	All angles less than 90°	1 angle equal to xc°

Obtuse Angle

Since we are learning here well-nigh an obtuse-angled triangle, thus it is necessary to know, what actually an obtuse angle is?

In that location are basically three types of angles formed when we bring together whatsoever two-line segments end to cease. They are:

Astute angle
Right angle
Obtuse angle

An astute angle is formed when two line segments are joined in such a way, that the angle between them is less than 90°. The triangle resulting from this angle is called an acute angle triangle.

A right angle is formed when one line segment is exactly perpendicular to another line segment at the joining points.

Likewise, read: Right Angle Triangle

Now, when we speak virtually the birdbrained bending, two line segments are joined in such a way that the angle between them is more xc°. And when we join the other 2 open ends of the line segments, then it results in an obtuse-angled triangle.

Obtuse Angled Triangle Formula

The formula for the expanse and perimeter of an obtuse triangle is similar to the formula for any other triangle.

Hence, the area of the triangle is given by:

Expanse = one/ii × b × h

where b is the base and h is the height of the triangle.

\(\brainstorm{array}{l}A=\sqrt{south(s-a)(s-b)(s-c)}sq.units\end{assortment} \)

Where s = (a+b+c)/2 (s= semiperimeter)

where a, b and c are the length of the sides of the triangle.

The perimeter of the triangle is always equal to the sum of the sides of the triangle. Hence, if a, b and c are the sides of the birdbrained triangle, and then the perimeter is given past;

Perimeter = a+b+c

How exercise you know if a triangle is obtuse

If any 2 angles of a triangle are given, information technology tin can be easily determined whether the triangle is an birdbrained triangle or non. Merely how to determine this, when the three sides of the triangle are known? We take inequality in the lines of Pythagorean identity to test this.

The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.

Let a, b and c are the lengths of the sides of triangle ABC and c is the largest side, and then the triangle is obtuse if

a² + b² < c²

Birdbrained Angled Triangle Properties

The sum of the two angles other than the obtuse angle is less than 90°.
The side reverse the birdbrained angle is the longest side of the triangle.
An obtuse triangle will have one and simply one birdbrained angle. The other ii angles are acute angles.
The points of concurrency, the Circumcenter and the Orthocenter lie outside of an obtuse triangle, while Centroid and Incenter lie inside the triangle.

Example

Triangle ABC is a perfect instance to study the triangle type – Obtuse.

Obtuse Angle Triangle

In triangle ABC, interior angle ACB =37°, which is less than ninety°, so it's an acute angle.
Interior bending ABC = 96°, which is more than ninety° and so, information technology'due south an obtuse angle.

Interior angle BAC=47°, which is less than 90°, so information technology'southward an acute angle.

As this triangle, ABC has ane angle (ABC=96°) more than 90°, so this triangle is obtuse.

Video Lesson on Types of Triangles

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