Identifying Triangles (by angle)

Front

What are the three types of triangles based on angles?

Back

The three types of triangles based on angles are acute triangles (all angles less than 90°), right triangles (one angle equal to 90°), and obtuse triangles (one angle greater than 90°).

Front

What defines an acute triangle?

Back

An acute triangle is defined as a triangle where all three interior angles are less than 90°.

Front

What defines a right triangle?

Back

A right triangle is defined as a triangle that has one angle equal to 90°.

Front

What defines an obtuse triangle?

Back

An obtuse triangle is defined as a triangle that has one angle greater than 90°.

Front

How can you identify a right triangle using the Pythagorean theorem?

Back

A triangle is a right triangle if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

What is the sum of the interior angles of any triangle?

Back

The sum of the interior angles of any triangle is always 180°.

Front

Can a triangle have more than one obtuse angle?

Back

No, a triangle cannot have more than one obtuse angle because the sum of the angles would exceed 180°.

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, one angle is 90°, and the sum of the other two angles must be 90°.

Front

What is an example of an application-based question involving triangles?

Back

An example of an application-based question is: 'Given a triangle with angles measuring 30° and 60°, what type of triangle is it?' The answer would be an acute triangle.

Front

How can you determine if a triangle is obtuse using its angles?

Back

You can determine if a triangle is obtuse by checking if one of its angles measures greater than 90°.