Geometry Triangle Relationships

Front

What is a triangle?

Back

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Front

What are the types of triangles based on sides?

Back

1. Equilateral Triangle: All sides are equal. 2. Isosceles Triangle: Two sides are equal. 3. Scalene Triangle: All sides are different.

Front

What are the types of triangles based on angles?

Back

1. Acute Triangle: All angles are less than 90 degrees. 2. Right Triangle: One angle is exactly 90 degrees. 3. Obtuse Triangle: One angle is greater than 90 degrees.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: c² = a² + b².

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How do you find the length of a side in a triangle using the Pythagorean theorem?

Back

To find the length of a side, rearrange the Pythagorean theorem: a = √(c² - b²) or b = √(c² - a²).

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. This is known as the Angle-Side Relationship.

Front

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

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is the concept of triangle congruence?

Back

Two triangles are congruent if they have the same size and shape, which can be proven using criteria like SSS, SAS, ASA, AAS, or HL.