Triangle Classifications and Properties

What is the definition of a scalene triangle?

What is the definition of an isosceles triangle?

What defines an equilateral triangle?

What is the definition of an acute triangle?

What defines a right triangle?

What is the definition of an obtuse triangle?

What is the definition of an equiangular triangle?

The distance formula is used to find _____ between two points.

How do you find the sides of a triangle using the distance formula and determine if it's a right angle?

Triangle Classifications

Scalene: A triangle with no sides that are congruent, meaning all sides have different lengths.
Isosceles: Features at least two sides that are congruent, which results in two equal angles opposite those sides.
Equilateral: All three sides are congruent, leading to all three angles also being congruent at 60 degrees each.

Angle Classifications

Acute: A triangle where all three angles are acute, each measuring less than 90 degrees.
Right: Contains one right angle that measures exactly 90 degrees, while the other two angles are acute.
Obtuse: Includes one obtuse angle, which measures more than 90 degrees but less than 180 degrees.

Additional Terminology

Equiangular: A triangle in which all three angles are congruent, each being 60 degrees in the case of equilateral triangles.

Distance Formula Usage

The distance formula is essential for finding the lengths of the sides of a triangle using the coordinates of its vertices.

Right Angle Determination

Check for right angles by using slopes (rise/run) to identify perpendicular lines; if two lines have negative reciprocal slopes, they form a right angle.
Solve for side lengths using the distance formula and keep the results in radical form to ensure accuracy.

Explore the different classifications of triangles based on their sides and angles. This quiz covers scalene, isosceles, equilateral, acute, right, and obtuse triangles, along with essential terminologies such as equiangular and the distance formula for calculation. Test your understanding of these geometric concepts!