Geometry Chapter 7 Flashcards
20 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a ratio?

  • A comparison of two quantities using division (correct)
  • A comparison of two quantities using addition
  • An expression without any comparison
  • A method for calculating areas

    • What is an extended ratio?

  • Can only compare two quantities
  • Can compare three or more quantities (correct)
  • Is always a whole number
  • Is not useful in geometry

    • What does 3:4:5 represent?

    It can be written as 3x:4x:5x and solved as an algebraic equation.

    A ______ is two fractions set equal to each other.

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

    What should you compare when looking at two triangles?

    <p>The extremes to the means in each triangle.</p> Signup and view all the answers

    What are the means in a proportion?

    <p>The inner two numbers in a proportion.</p> Signup and view all the answers

    What are the extremes in a proportion?

    <p>The outer two numbers in a proportion.</p> Signup and view all the answers

    Cross products in a proportion are equal.

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

    What does the cross product property state?

    <p>The product of the extremes equals the products of the means.</p> Signup and view all the answers

    What do similar polygons have in common?

    <p>They are the same shape</p> Signup and view all the answers

    In similar polygons, corresponding angles are congruent.

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

    What is the scale factor in similar polygons?

    <p>The ratio of the lengths of the corresponding sides.</p> Signup and view all the answers

    The ratio of the perimeters of similar polygons equals the ratio of the sides.

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

    Angle-angle similarity means triangles are similar when two angles are congruent.

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

    What similarity relationships work for triangles?

    <p>Side-side-side similarity and angle-angle similarity</p> Signup and view all the answers

    What is a midsegment of a triangle?

    <p>A segment with endpoints that are the midpoints of two sides of the triangle.</p> Signup and view all the answers

    The triangle midsegment theorem states that a midsegment is parallel to one side of the triangle.

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

    What does the triangle proportionality theorem describe?

    <p>The proportionality relationships within triangles.</p> Signup and view all the answers

    What is the property of proportional parts of parallel lines?

    <p>They cut off the transversals proportionally.</p> Signup and view all the answers

    What do congruent parts of parallel lines imply?

    <p>They cut off congruent segments on every side.</p> Signup and view all the answers

    Study Notes

    Ratios and Proportions

    • Ratio: A comparison of two quantities through division.
    • Extended Ratio: Compares three or more quantities.
    • 3:4:5: Can be represented as 3x:4x:5x; used in triangular problems, set equal to 180 or another specified number.
    • Proportion: Two fractions that are set equal to each other.
    • Cross Products: The products of the extremes and means in a proportion must be equal.
    • Cross Product Property: In a proportion, the product of the extremes equals the product of the means.

    Triangle Similarity

    • Similar Polygons: Same shape with proportional side lengths; sizes may differ.
    • Corresponding Angles: In similar polygons, these angles are congruent.
    • Scale Factor: The ratio of lengths of corresponding sides in similar polygons.
    • Perimeters: The ratio of perimeters equals the ratio of the corresponding sides.

    Triangle Properties

    • Angle Angle Similarity: Two triangles are similar if two angles are congruent.
    • Side-Side-Side (SSS) Similarity: Triangles are similar if the corresponding side lengths are proportional.
    • Side-Angle-Side (SAS) Similarity: If one angle is congruent and the sides enclosing the angle are proportional, the triangles are similar.
    • Triangle Proportionality Theorem: Discussed in Chapter 7, Section 4.
    • Converse of Triangle Proportionality Theorem: Also detailed in Section 7-4.

    Triangle Segments

    • Midsegment of a Triangle: A segment connecting the midpoints of two sides of a triangle.
    • Triangle Midsegment Theorem: A midsegment is parallel to one side and half the length of that side.

    Parallel Lines and Proportionality

    • Proportional Parts of Parallel Lines: If three or more parallel lines intersect two transversals, they cut off segments proportional to one another.
    • Congruent Parts of Parallel Lines: If three or more parallel lines cut off congruent segments on one transversal, they will also cut off congruent segments on all transversals.

    Special Segments in Similar Triangles

    • Altitude Ratios: The ratio of altitudes in similar triangles is the same as the ratio of their sides.
    • Angle Bisectors and Medians: Ratios of these segments also reflect the ratio of the sides in similar triangles.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Explore essential concepts from Geometry Chapter 7 with these flashcards. Each card provides definitions for key terms like ratio, extended ratio, and proportions, aiding in your understanding of geometric relationships. Perfect for quick review and study.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser