Side Lengths of Triangles

Flashcards covering the Triangle Inequality Theorem, triangle classification by sides, and the relationship between side lengths and angle measures.

Triangle Inequality Theorem

A theorem stating that for a triangle to be formed, the sum of any two side lengths must be greater than the length of the third side.

Unique Triangle

If three line segments satisfy the conditions of the Triangle Inequality Theorem, exactly one unique triangle is formed.

Equilateral

A term used to classify a triangle when all three sides are equal.

Isosceles

A term used to classify a triangle when at least two sides are equal.

Scalene

A term used to classify a triangle when none of the sides are equal.

Longest Side Relationship

In any triangle, the longest side is located opposite the largest angle.

Shortest Side Relationship

In any triangle, the shortest side is located opposite the smallest angle.

Third Side Range Example

For a triangle with side lengths of $7\,cm$ and $9\,cm$, the third side $AC$ must be such that $2 < AC < 16$.

Opposite Side of Angle A

The specific line segment in triangle $ABC$ identified as Side $BC$.

Opposite Side of Angle B

The specific line segment in triangle $ABC$ identified as Side $AC$.

Opposite Side of Angle C

The specific line segment in triangle $ABC$ identified as Side $AB$.