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. (A)</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. (C)</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°. (D)</p> Signup and view all the answers

What is the effect of dilations on parallel lines?

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

What is a key property of dilations regarding figure orientation?

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

Which angles are formed when a transversal intersects two lines?

<p>Vertical and corresponding angles. (C)</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. (B)</p> Signup and view all the answers

What does a scale factor greater than 1 indicate?

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

Which of the following scenarios demonstrates a reduction in size?

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

Which equation correctly represents the calculation of a scale factor?

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

What is the area of the dilated rectangle?

<p>1000 $cm^{2}$ (D)</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 (B)</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 (B)</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 (C)</p> Signup and view all the answers

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

<p>2 (B)</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 (A)</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 (A)</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 (C)</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 (C)</p> Signup and view all the answers

What characteristic do congruent figures share?

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

Which of the following is true for similar figures?

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

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

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

Which of the following statements about congruent triangles is false?

<p>They can have different dimensions. (A)</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}$ (C)</p> Signup and view all the answers

What indicates a positive slope on a graph?

<p>The graph line goes from left to right. (C)</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. (C)</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. (A)</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. (A)</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. (D)</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. (A)</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. (D)</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. (A)</p> Signup and view all the answers

Which statement about zero slope is true?

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

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

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

What does congruent mean in geometry?

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

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

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

Which of the following best describes similar figures?

<p>They have proportional sizes and corresponding sides. (C)</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. (B)</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 (A)</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 (B)</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 (C)</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. (D)</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 (C)</p> Signup and view all the answers

Flashcards

Transversal

A line that intersects two other lines at distinct points.

Intersecting Lines

Lines that cross at a specific point.

Angles formed by a Transversal

Angles created when a transversal intersects two lines.

Corresponding Angles

Angles that have the same relative position at each intersection.

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Equal Angles

Angles that have the same measure.

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Scale Factor

A multiplier that changes the size of a figure, either enlarging or reducing it.

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Scale Factor Calculation

Calculated by dividing the new size by the original size.

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Enlargement Scale Factor

Scale factor is greater than 1.

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Reduction Scale Factor

Scale factor is less than 1.

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Scale Factor Example

A number that describes how much a figure is enlarged or reduced in comparison to the original figure.

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Dilated Rectangle Dimensions

The dimensions of a rectangle that has been enlarged or reduced using a scale factor.

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Scale Factor

A ratio comparing the corresponding sides of a dilated figure to the original figure.

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Area of a Rectangle

The space enclosed within a rectangle. Calculated by multiplying its width and length.

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Scale Factor = 5/2

A scale factor of 5/2 means the dilated rectangle's sides are 5/2 times the original.

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Original Dimensions (16 cm by 10 cm)

Starting measurements of a rectangle

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Dilated Dimensions (40 cm by 25 cm)

New measurements of the rectangle after applying the scale factor.

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Area of Dilated Rectangle

Area of dilated shape = 1000 cm²

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Congruent Figures

Figures that have exactly the same size and shape.

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Similar Figures

Figures that have the same shape but not necessarily the same size.

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Proportional Sides

Corresponding sides of similar figures maintain a constant ratio.

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Scale Factor

The ratio of corresponding sides of similar figures.

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Corresponding Sides of Similar Figures

Sides in similar figures occupying the same relative positions.

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Same Angles of Similar Figures

Similar figures have the same angles, though not necessarily the same side lengths.

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Scale Factor

A multiplier that enlarges or reduces a figure.

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Enlargement

A scale factor greater than one.

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Reduction

A scale factor between zero and one.

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Congruent

Figures with the same shape and size.

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Dilations

Transformations that change the size of a figure, but not its shape.

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Angle measure in Dilations

Angles remain the same.

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Parallel lines in Dilations

Parallel lines remain parallel.

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Points in Dilations

The position of points remain the same.

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Orientation in Dilations

Figure orientation remains the same.

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Similar Figures

Figures that have the same shape, not necessarily the same size.

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Dilations and Similar Figures

Dilations create similar figures.

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Similar Triangles

Triangles with the same shape, but not necessarily the same size.

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Scale Factor

The ratio of corresponding side lengths in similar figures.

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Proportions in Similar Triangles

Corresponding sides of similar triangles are in proportion.

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Finding Unknown Side Length

Using proportions from similar triangles to find a missing side length.

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Ratio of Sides

A comparison of two or more quantities, specifically sides in similar triangles.

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Solving Proportions

Using cross-multiplication or equivalent methods to solve for an unknown quantity in a proportion.

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Positive Slope

A graph line that goes up from left to right. As x increases, y increases.

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Negative Slope

A graph line that goes down from left to right. As x increases, y decreases.

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Zero Slope

A horizontal line on a graph. The y-value stays the same as the x-value changes.

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Undefined Slope

A vertical line on a graph. The x-value stays the same as the y-value changes.

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Slope of a Line

The steepness of a line.

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Mixed Number Addition

Adding fractions with whole number parts

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Fraction Division

Dividing one fraction by another fraction

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Rise

Vertical change between two points on a line.

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Run

Horizontal change between two points on a line.

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Congruent Figures

Figures with exactly the same size and shape

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Finding Slope

Calculate the slope using the 'rise over run' formula.

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Similar Figures

Figures with the same shape, but not necessarily the same size

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Start Right Point

Choosing the starting point on the line for calculating the slope.

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Proportional Sides

Corresponding sides of similar figures have a constant ratio

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Ratio Equation

A mathematical equation expressing a proportion

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Solving for x

Finding the value of a variable that makes an equation true

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