Triangle Similarity and Transformations

Study Notes

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.

Description

This quiz covers the essential concepts of triangle similarity, including AA, SSS, and SAS similarity criteria. Additionally, it explores the properties of similarity and basic geometric transformations like mapping and reflection. Test your understanding of these fundamental geometric principles.