Geometry Vocab Chapter 7

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Questions and Answers

What is a ratio?

A comparison of two quantities using division.

What is an extended ratio?

Ratios that are used to compare three or more quantities.

What is a proportion?

An equation of the form a/b = c/d that states that the two ratios are equal.

What are the extremes in the proportion a/b = c/d?

The numbers a and d. Signup and view all the answers

What are the means in the proportion a/b = c/d?

The numbers b and c. Signup and view all the answers

What is the cross product in the proportion a/b = c/d?

The cross products are ad and bc. Signup and view all the answers

What are similar polygons?

Polygons that have congruent corresponding angles and proportional corresponding side lengths. Signup and view all the answers

What is a similarity ratio?

The scale factor between two similar polygons. Signup and view all the answers

What is a scale factor?

The ratio of the lengths of two corresponding sides of two similar polygons or two similar solids. Signup and view all the answers

What is the midsegment of a triangle?

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

What is a similarity transformation?

When a figure and its transformation image are similar. Signup and view all the answers

What is the center of dilation?

The point from which dilations are performed. Signup and view all the answers

What is the scale factor of a dilation?

The ratio of a length on an image to a corresponding length on the preimage. Signup and view all the answers

What is a dilation?

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

What is an enlargement?

A dilation with a scale factor greater than one. Signup and view all the answers

What is a reduction?

A dilation with a scale factor between zero and one. Signup and view all the answers

What is a scale model?

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

What is scale?

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

Study Notes

Geometry Vocabulary Study Notes

Ratio: A mathematical comparison between two quantities using division to express their relative sizes.
Extended Ratio: A type of ratio that compares three or more quantities, enhancing the basic concept of a simple ratio.
Proportion: A statement that equates two ratios, represented in the form a/b = c/d, indicating their equality.
Extremes: In the proportion a/b = c/d, the extremes are the first and last terms (a and d), which are compared.
Means: In the proportion a/b = c/d, the means are the middle terms (b and c), serving as the link between extremes.
Cross Product: Refers to products ad and bc in the proportion a/b = c/d. The proportion holds true when these cross products are equal.
Similar Polygons: These polygons feature congruent corresponding angles and proportional corresponding side lengths, ensuring they retain a consistent shape.
Similarity Ratio: The scale factor derived from comparing two similar polygons, illustrating their dimensional relationship.
Scale Factor: The ratio that describes the lengths of two corresponding sides between similar polygons or solids, indicating how much one is enlarged or reduced from the other.
Midsegment of a Triangle: A line segment that connects the midpoints of two sides of a triangle, creating certain proportional relationships.
Similarity Transformation: A transformation in which a geometric figure and its image maintain similarity, preserving shapes but not necessarily sizes.
Center of Dilation: The specific point from which a dilation transformation originates, acting as a pivot for enlargements or reductions.
Scale Factor of a Dilation: The ratio comparing a length on the transformed image to a corresponding length on the original figure, crucial for determining the effect of the dilation.
Dilation: A transformation that proportionally enlarges or reduces an original figure, maintaining its shape through scaling.
Enlargement: A type of dilation where the scale factor is greater than one, resulting in an increased size of the figure.
Reduction: A form of dilation with a scale factor between zero and one, leading to a decrease in the size of the figure.
Scale Model: An object crafted to maintain proportional dimensions relative to the actual object it represents, aiding in visualization and representation.
Scale: The ratio that compares a length on a model or drawing to its actual counterpart, fundamental for accurate representation in models or plans.

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Description

Test your knowledge of key vocabulary terms from Geometry Chapter 7. This quiz covers essential concepts such as ratios, proportions, and their components. Perfect for students looking to reinforce their understanding of geometric relationships.