Geometry Chapter 7 Flashcards

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?

Exchange your means and the proportion is still true. Signup and view all the answers

What is the Reciprocal Property?

a/b = c/d ----> b/a = d/c. Signup and view all the answers

Explain the Add One Property.

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

When are two polygons considered similar?

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

What is a Scale Factor?

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

All regular polygons are similar.

True Signup and view all the answers

Two equilateral triangles are sometimes similar.

False Signup and view all the answers

A right triangle and an obtuse triangle can be similar.

False Signup and view all the answers

Two equilateral pentagons are similar.

False Signup and view all the answers

What is the AA Similarity Postulate?

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

Define the SAS Similarity Theorem.

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. Signup and view all the answers

What is the SSS Similarity Theorem?

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

What does the Triangle Proportionality Theorem state?

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

Explain the Transversal Theorem.

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

What is the Ray Theorem?

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. 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.