Triangle Inequality - Honors

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given side lengths of a triangle, how can you determine if a triangle can exist?

Back

To determine if a triangle can exist with given side lengths a, b, and c, check if a + b > c, a + c > b, and b + c > a.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

How do you find the smallest angle in a triangle given the side lengths?

Back

To find the smallest angle in a triangle, identify the shortest side and use the Law of Cosines or the properties of triangles to calculate the angle.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab * cos(C).

Front

How can you determine which two points (or towers) are closest together in a triangle?

Back

To determine which two points are closest together, identify the two smallest angles or the two shortest sides of the triangle.

Front

What is the significance of the longest side in a triangle?

Back

The longest side of a triangle is crucial for determining the triangle's properties, including the largest angle and the feasibility of forming a triangle.

Front

How do you order the sides of a triangle from longest to shortest?

Back

To order the sides of a triangle from longest to shortest, measure the lengths of each side and arrange them in descending order.

Front

What is the relationship between the angles in a triangle?

Back

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

Front

How can you apply the Triangle Inequality Theorem to real-world problems?

Back

The Triangle Inequality Theorem can be applied in various real-world scenarios, such as determining the feasibility of constructing a triangle with given lengths or analyzing distances between points.