Geometry Chapter 7: Similarity Flashcards

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Questions and Answers

What is a ratio?

A comparison of 2 shapes

A comparison of 2 quantities using addition

A type of geometric figure

A comparison of 2 quantities using division (correct)

What are cross products?

The differences of the extremes and the means

The products of the extremes and the means (correct)

The sums of the extremes and the means

The ratios of the extremes to the means

In the proportion a/b = c/d, what are the extremes?

a and d

In the proportion a/b = c/d, what are the means?

b and c Signup and view all the answers

What is a proportion?

An equation stating that 2 ratios are equal Signup and view all the answers

What is a scale factor?

The ratio of the lengths of the corresponding sides of 2 similar polygons Signup and view all the answers

Similar polygons have the same shape but not necessarily the same size.

True Signup and view all the answers

What is the midsegment of a triangle?

A segment with endpoints that are the midpoints of 2 sides of the triangle Signup and view all the answers

What is dilation?

A transformation that enlarges or reduces the original figure proportionally Signup and view all the answers

An enlargement is a dilation with a scale factor less than 1.

False Signup and view all the answers

A reduction is a dilation with a scale factor greater than 1.

False Signup and view all the answers

What is a scale in geometry?

The ratio of a length on the model or drawing to the actual length of the object being drawn Signup and view all the answers

What is a scale model?

An object or drawing with lengths proportional to the object it represents Signup and view all the answers

What is a similarity transformation?

A dilation that produces a similar figure Signup and view all the answers

What is an altitude in a triangle?

A segment from the vertex of a triangle to the opposite side which is perpendicular to it Signup and view all the answers

What is an angle bisector?

A line that divides an angle into two congruent angles Signup and view all the answers

What is a median in geometry?

A segment from a vertex to the midpoint of the opposite side Signup and view all the answers

Study Notes

Key Concepts of Similarity in Geometry

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 and Components of Proportions

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 and Similarity in Polygons

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.

Triangle Properties

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.

Transformations and Dilation

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.

Additional Geometric Terminology

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.

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Description

Test your understanding of key concepts in Geometry Chapter 7 on Similarity with these flashcards. Learn important definitions related to ratios, proportions, and the properties of similar figures through concise explanations.