Geometry Chapter 7: Similarity Flashcards

Ratio: A mathematical expression comparing two quantities via division, essential for understanding proportions.
Proportion: An equation that asserts the equality of two ratios, forming the basis for many geometric relationships.

Cross Products: Products calculated from the extremes (first and last terms) and the means (middle terms) of a proportion, used to check for equivalence.
Extremes: In the proportion a/b = c/d, the values a and d are referred to as extremes, crucial for setting up and solving proportions.
Means: In the same proportion a/b = c/d, the values b and c are called means, playing a critical role in maintaining the equality of ratios.

Scale Factor: Represents the ratio between the lengths of corresponding sides of two similar polygons, determining their relative size.
Similar Polygons: These polygons maintain the same shape but differ in size, a core concept in understanding geometric transformations.

Midsegment of a Triangle: A segment connecting the midpoints of two sides, indicating properties related to triangle similarity and area.
Altitude: Defined as a line segment from a triangle’s vertex to the opposite side, forming a right angle, important for calculating area.

Dilation: A transformation that scales a figure either up or down while preserving proportions, fundamental in creating similar figures.
Enlargement: Occurs when a dilation's scale factor is greater than 1, resulting in a larger figure.
Reduction: Happens when the scale factor of a dilation is less than 1, creating a smaller version of the original figure.
Similarity Transformation: Involves dilations that yield figures that are similar, emphasizing proportional relationships.

Scale: The ratio used to compare a length in a model or drawing to the actual object, key for accurate representations.
Scale Model: A representation in which dimensions are proportional to the real object, allowing for detailed study and comparison.
Angle Bisector: A line segment that divides an angle into two equal angles, important for angle relationships in polygons.
Median: A line segment drawn from a vertex to the midpoint of the opposite side, essential for centroid calculations and triangle properties.