Geometry Chapter 7 Flashcards
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Questions and Answers

What is a ratio?

The ratio of one number to another is the quotient when the first number is divided by the second.

What is a proportion?

Stating two ratios are equal.

What is the Cross Product in the context of proportions?

Product of your extremes = product of your means.

What does the Exchange Property state?

<p>Exchange your means and the proportion is still true.</p> Signup and view all the answers

What is the Reciprocal Property?

<p>a/b = c/d ----&gt; b/a = d/c.</p> Signup and view all the answers

Explain the Add One Property.

<p>a+b/b = c+d/d (a/b + b/b, c/d + d/d).</p> Signup and view all the answers

When are two polygons considered similar?

<p>Two polygons are similar if their vertices can be paired so that corresponding angles are congruent and corresponding sides are in proportion.</p> Signup and view all the answers

What is a Scale Factor?

<p>Ratio/proportion of the lengths of 2 corresponding sides of similar figures.</p> Signup and view all the answers

All regular polygons are similar.

<p>True</p> Signup and view all the answers

Two equilateral triangles are sometimes similar.

<p>False</p> Signup and view all the answers

A right triangle and an obtuse triangle can be similar.

<p>False</p> Signup and view all the answers

Two equilateral pentagons are similar.

<p>False</p> Signup and view all the answers

What is the AA Similarity Postulate?

<p>If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.</p> Signup and view all the answers

Define the SAS Similarity Theorem.

<p>If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.</p> Signup and view all the answers

What is the SSS Similarity Theorem?

<p>If the sides of two triangles are in proportion, then the triangles are similar.</p> Signup and view all the answers

What does the Triangle Proportionality Theorem state?

<p>If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.</p> Signup and view all the answers

Explain the Transversal Theorem.

<p>If three parallel lines intersect two transversals, then they divide the transversals proportionally.</p> Signup and view all the answers

What is the Ray Theorem?

<p>If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.</p> Signup and view all the answers

Study Notes

Key Geometry Concepts

  • Ratio: Quotient when one number is divided by another; used to compare sizes of two quantities.

  • Proportion: An expression indicating that two ratios are equal, crucial for solving many geometric problems.

  • Cross Product: Method for proving proportions; states that the product of the extremes equals the product of the means.

  • Exchange Property: A property indicating that swapping the means in a proportion does not change its validity.

  • Reciprocal Property: Demonstrates the relationship between two ratios; if a/b equals c/d, then b/a equals d/c.

  • Add One Property: Allows addition of the same number to both denominators of two ratios while maintaining the equality of the proportions.

Polygons and Similarity

  • Similar Polygons: Polygons whose corresponding angles are congruent and corresponding sides are in proportion.

  • Scale Factor: The ratio of the lengths of two corresponding sides in similar figures, determining their relative size.

  • Regular Polygons: Defined as both equiangular and equilateral; all regular polygons are similar, regardless of size.

  • Equilateral Triangles: Always similar due to having identical angles.

  • Isosceles Triangles: Sometimes similar, depending on the angles they contain.

  • Right Triangle vs. Obtuse Triangle: These two triangle types are never similar due to differing angle measures.

  • Equilateral Pentagons: Two equilateral pentagons are not considered similar despite equal angles.

Theorems and Postulates

  • AA Similarity Postulate: If two angles of one triangle are congruent to two angles of another triangle, the triangles are confirmed to be similar.

  • SAS Similarity Theorem: If an angle of one triangle is congruent to an angle of another triangle, and the sides including these angles are proportional, then the triangles are similar.

  • SSS Similarity Theorem: States that if the sides of two triangles are proportional, then the triangles are similar.

Proportionality Theorems

  • Triangle Proportionality Theorem: If a line parallel to one triangle’s side intersects the other two sides, it divides those sides proportionally.

  • Transversal Theorem: States that if three parallel lines intersect two transversal lines, they divide those lines proportionally.

  • Ray Theorem: A ray that bisects an angle within a triangle creates segments on the opposite side that are proportional to the other two sides’ lengths.

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Enhance your understanding of geometry concepts with these Chapter 7 flashcards. Each card provides key definitions including ratio, proportion, and more. Perfect for mastering the intricate relationships found in geometric studies.

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