Geometry Dilations and Transversals Quiz
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Questions and Answers

What does a scale factor of K = 0.5 represent?

  • No change in size
  • A reduction (correct)
  • An enlargement
  • Congruent figures

    • Which statement about angle measures during dilations is true?

  • They decrease in size.
  • They remain the same. (correct)
  • They increase in size.
  • They become congruent with the original figure.

    • What defines a transversal in geometry?

  • A line that intersects two straight lines at different angles.
  • A line that intersects two straight lines at distinct points. (correct)
  • A line that is perpendicular to two straight lines.
  • A line that runs parallel to two straight lines.

    • If angle ∠1 is equal to angle ∠3, what relationship do they form?

    <p>They are corresponding angles.</p> Signup and view all the answers

    If a figure has a scale factor of K = 1, what happens to the figure?

    <p>It remains congruent to the original figure.</p> Signup and view all the answers

    If angle ∠2 measures 179°, what can be concluded about angle ∠4?

    <p>Angle ∠4 is also 179°.</p> Signup and view all the answers

    What is the effect of dilations on parallel lines?

    <p>They remain parallel.</p> Signup and view all the answers

    What is a key property of dilations regarding figure orientation?

    <p>It remains the same.</p> Signup and view all the answers

    Which angles are formed when a transversal intersects two lines?

    <p>Vertical and corresponding angles.</p> Signup and view all the answers

    What total value is likely represented by the angles if one angle measures 180°?

    <p>The total of angles on a straight line.</p> Signup and view all the answers

    What does a scale factor greater than 1 indicate?

    <p>It enlarges the size of an object.</p> Signup and view all the answers

    If the original size of a figure is 15 and the new size is 45, what is the scale factor?

    <p>3</p> Signup and view all the answers

    Which of the following scenarios demonstrates a reduction in size?

    <p>New size 6, Original size 12</p> Signup and view all the answers

    Which equation correctly represents the calculation of a scale factor?

    <p>Scale Factor = New / Original</p> Signup and view all the answers

    What is the scale factor if the New size is 50 and the Original size is 25?

    <p>2</p> Signup and view all the answers

    What are the dimensions of the dilated rectangle after applying the scale factor of $ rac{5}{2}$?

    <p>40 cm by 25 cm</p> Signup and view all the answers

    What is the area of the dilated rectangle?

    <p>1000 $cm^{2}$</p> Signup and view all the answers

    Which operation is used to find the dimensions of the dilated rectangle?

    <p>Multiplying the original dimensions by the scale factor</p> Signup and view all the answers

    If the scale factor was doubled to $ rac{10}{2}$, what would the new width of the rectangle be?

    <p>50 cm</p> Signup and view all the answers

    What is the main mathematical concept used to find the area of the dilated rectangle?

    <p>Multiplication of dimensions</p> Signup and view all the answers

    What is the scale factor between triangle ABC and triangle A'B'C'?

    <p>2</p> Signup and view all the answers

    What is the value of the unknown side length $x$ in triangle A'B'C'?

    <p>5.6</p> Signup and view all the answers

    How do the side lengths of triangle ABC relate in proportion to triangle A'B'C'?

    <p>They are directly proportional</p> Signup and view all the answers

    What does the equation $ rac{A'B'}{AB} = rac{A'C'}{AC}$ represent?

    <p>A proportion of corresponding side lengths</p> Signup and view all the answers

    Which of the following is a necessary step when finding side lengths in similar triangles?

    <p>Setting up a proportion</p> Signup and view all the answers

    What characteristic do congruent figures share?

    <p>Same size</p> Signup and view all the answers

    Which of the following is true for similar figures?

    <p>They can be transformed into each other</p> Signup and view all the answers

    What is the scale factor between triangle ABC and triangle A'B'C'?

    <p>$ rac{4}{5}$</p> Signup and view all the answers

    Which of the following statements about congruent triangles is false?

    <p>They can have different dimensions.</p> Signup and view all the answers

    In the given triangles, which sides' proportions correctly represent their similarity?

    <p>$ rac{4}{5}$, $ rac{8}{6}$, $ rac{12}{9}$</p> Signup and view all the answers

    What indicates a positive slope on a graph?

    <p>The graph line goes from left to right.</p> Signup and view all the answers

    What happens to the y-axis in a graph with a negative slope?

    <p>The y-axis decreases as the x-axis increases.</p> Signup and view all the answers

    Which of the following describes a negative slope?

    <p>The graph line goes down from left to right.</p> Signup and view all the answers

    Which of the following statements about the x-axis in a positive slope is correct?

    <p>The x-axis increases while the y-axis increases.</p> Signup and view all the answers

    How does the y-axis behave in a scenario where the x-axis is increasing?

    <p>It may either increase or decrease depending on the slope.</p> Signup and view all the answers

    What characterizes a graph with zero slope?

    <p>The graph moves side to side with a constant y-value.</p> Signup and view all the answers

    What effect does a vertical slope have on the graph?

    <p>The y-value increases with a constant x-value.</p> Signup and view all the answers

    In which scenario would a graph exhibit an undefined slope?

    <p>The graph goes straight up and down.</p> Signup and view all the answers

    Which statement about zero slope is true?

    <p>It results in a horizontal line in the graph.</p> Signup and view all the answers

    If the x-value is constant, what happens to the y-value in a vertical slope?

    <p>The y-value may increase or decrease.</p> Signup and view all the answers

    What is the result of adding $3 rac{1}{2}$ and $5 rac{1}{2}$?

    <p>$19 rac{1}{4}$</p> Signup and view all the answers

    What does congruent mean in geometry?

    <p>The angles and sides are the same size and length.</p> Signup and view all the answers

    If $ rac{102}{x} = rac{7}{9}$, what is the value of $x$?

    <p>$14.57$</p> Signup and view all the answers

    Which of the following best describes similar figures?

    <p>They have proportional sizes and corresponding sides.</p> Signup and view all the answers

    For the triangles shown, if one triangle has sides labeled 9 and 7, and the other has 27 and an unknown side, which relationship is true?

    <p>The triangles are similar due to proportional sides.</p> Signup and view all the answers

    What does the term 'rise' refer to when calculating the slope of a line?

    <p>The vertical distance between two points</p> Signup and view all the answers

    If the rise is 4 and the run is 2, what is the slope of the line?

    <p>2</p> Signup and view all the answers

    What is the correct formula to calculate the slope of a line?

    <p>Change in y / Change in x = Slope</p> Signup and view all the answers

    Which of the following statements is true about the slope of a horizontal line?

    <p>The slope is zero.</p> Signup and view all the answers

    What is meant by the term 'run' in the context of finding the slope?

    <p>The distance traveled horizontally</p> Signup and view all the answers

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