Geometry Chapter 7 Test Flashcards

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Questions and Answers

What is a ratio?

A comparison of 2 things.

What is a proportion?

2 equal ratios

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

B and C

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

A and D Signup and view all the answers

1:2:3 is an _ _.

extended ratio Signup and view all the answers

Can extended ratios be written as fractions?

False Signup and view all the answers

What do a/b=c/d, b/a=d/c, a/c=b/d, and a+b/b=c+d/d all multiply out to?

Bc=ad Signup and view all the answers

What does 'similar' mean in geometry?

Same shape Signup and view all the answers

Can similar polygons be congruent?

False Signup and view all the answers

What are the angles of similar polygons?

Equal to each other Signup and view all the answers

What are the sides of similar polygons?

In proportion to each other Signup and view all the answers

What is a scale factor in geometry?

What the proportional sides of polygons simplify to when the shapes are similar Signup and view all the answers

What is the arithmetic mean?

Add up and divide Signup and view all the answers

What is the geometric mean?

Multiply and take the square root Signup and view all the answers

If you have a triangle with its 3 angles in a ratio of 1:2:3, what would your equation be to find each of the angles? (Use x)

X + 2x + 3x = 180 Signup and view all the answers

What does AA~ mean in triangle similarity?

Two triangles are similar if two pairs of angles are congruent Signup and view all the answers

What does SSS~ indicate?

If the corresponding sides of two triangles are proportional, then the triangles are similar Signup and view all the answers

What does SAS~ signify?

Two sets of sides are proportional and two angles are congruent in two triangles Signup and view all the answers

What does CPSTP stand for?

Corresponding parts in similar triangles are in proportion Signup and view all the answers

What does the Side Splitter Theorem state?

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

What does the Triangle Angle Bisector Theorem state?

The bisector of an angle of a triangle divides the side it goes to proportionally with the two other sides. Signup and view all the answers

Study Notes

Ratios and Proportions

Ratios compare two quantities, illustrating their relative sizes.
A proportion represents two equal ratios, indicating a relationship between four quantities.
In the proportion a/b = c/d, B and C are called the means, while A and D are referred to as the extremes.

Extended Ratios

An extended ratio, such as 1:2:3, compares three or more quantities.
Extended ratios cannot be represented as simple fractions.

Properties of Proportions

Proportions lead to the equality of products: Bc = ad for the established ratios.
Similar polygons maintain angles that are equal and sides that correspond proportionally.

Similar Polygons

Similar polygons may be congruent, meaning they could have the same shape and size.
The sides of similar polygons must be in proportion, and the angles are equal.

Scale Factor

The scale factor illustrates the ratio of corresponding sides between similar figures.

Means of Calculation

The arithmetic mean of a set of numbers is found by summing the values and dividing by their count.
The geometric mean requires multiplying the numbers and taking the square root.

Triangle Angle Relationships

For a triangle with angles in the ratio 1:2:3, the equation representing the angles is x + 2x + 3x = 180.
Triangles are similar if two pairs of angles are congruent (AA similarity).
The SSS similarity criterion states that if the corresponding sides of two triangles are proportional, then those triangles are similar.
SAS similarity occurs when two sets of sides are proportional and two angles are congruent in two triangles.

Important Theorems

CPSTP (Corresponding Parts of Similar Triangles are in Proportion) underlines the proportional relationship of corresponding parts in similar triangles.
The Side Splitter Theorem indicates that a line parallel to one side of a triangle divides the other two sides proportionally.
The Triangle Angle Bisector Theorem establishes that an angle bisector divides the opposite side in proportion to the other two sides of the triangle.

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Description

Test your knowledge of key concepts in Geometry Chapter 7 with these flashcards. This quiz covers important terms such as ratios, proportions, and the concepts of means and extremes. Dive in and reinforce your understanding of these foundational geometric principles.