Obtuse Triangle

An obtuse triangle is a type of triangle where one of the angles is greater than 90 degrees. In other words, an obtuse triangle has one angle that is obtuse, meaning it measures more than 90 degrees. The other two angles in an obtuse triangle are acute, meaning they measure less than 90 degrees. The sum of the three angles in any triangle is always 180 degrees.

Properties of Obtuse Triangle:

• Has one angle greater than 90 degrees
• Other two angles are acute (less than 90 degrees)
• The sum of all three angles is always 180 degrees
• The longest side is opposite the obtuse angle

Example:

Let's consider a triangle with the following angle measures:

• Angle A = 100 degrees (obtuse angle)
• Angle B = 40 degrees (acute angle)
• Angle C = 40 degrees (acute angle)

In this example, Angle A measures 100 degrees, making it an obtuse angle. Angles B and C both measure 40 degrees, making them acute angles. The sum of all three angles is: 100 + 40 + 40 = 180 degrees, satisfying the property of a triangle.

Study Guide:

To understand obtuse triangles better, it's important to remember the following key points:

1. An obtuse triangle has one angle that measures more than 90 degrees.
2. The other two angles in an obtuse triangle are acute, measuring less than 90 degrees.
3. The sum of all three angles in a triangle is always 180 degrees.
4. The longest side of an obtuse triangle is always opposite the obtuse angle.

When working with obtuse triangles, it's helpful to use the properties to identify and classify triangles based on their angle measures.

Remember to practice identifying obtuse triangles and their properties through examples and exercises to solidify your understanding of this concept.