Triangle Similarity and Transformations

Triangle Similarity Concepts

• AA-similarity: Two triangles are similar if two corresponding angles are congruent.
• SSS-similarity: Two triangles are similar if the three sides of one triangle are proportional to the three corresponding sides of another triangle.
• SAS-similarity: Two triangles are similar if two pairs of sides are proportional and the included angles are congruent.

Properties of Similarity

• Reflexive property of similarity: A triangle is always similar to itself, denoted as △ABC~△ABC.
• Transitive property: If one triangle is similar to a second, and the second is similar to a third, then the first is also similar to the third (if △ABC~△DEF and △DEF~△XYZ, then △ABC~△XYZ).

Geometric Transformations

• Mapping: Shows how each point of one geometric figure corresponds to a point in another figure.
• Reflection: A transformation that creates a mirror image of a figure across a line, called the reflection line.
• Transformation: An operation that alters the position, size, or shape of a geometric figure, resulting in a new figure.

Mathematical Concepts

• Equation: A statement that shows the equality of two expressions, marked by an equals sign.
• Solution: The specific value(s) that satisfy a given equation.
• Solving an Equation: The process of determining the value of a variable that makes the equation true.
• Proportion: An equation that states two ratios are equal, often used to express relationships between quantities.

Triangle Properties

• Angle Sum: The sum of the interior angles of a triangle always equals 180 degrees.