Geometry Chapter 7 Test Flashcards
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Questions and Answers

What is a ratio?

a comparison of two quantities by division

What is a proportion?

an equation stating two ratios are equal

What is an extended ratio?

comparing three or more quantities

How do you calculate the sides of a triangle with the ratios 2:2:3 and a perimeter of 392?

<p>2x + 2x + 3x = 392</p> Signup and view all the answers

What do you do if the perimeter is not given but the ratios of the sides are?

<p>set the ratios of the sides to 180</p> Signup and view all the answers

What is a scale model?

<p>is an object or drawing with lengths proportional to the object it represents</p> Signup and view all the answers

What does dilation refer to in geometry?

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

What is a scale factor?

<p>3: 25(12) = 3:300 = 1:100</p> Signup and view all the answers

What defines similar polygons?

<p>same shape but not necessarily the same size</p> Signup and view all the answers

What is the first rule for similar polygons?

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

What is the second rule for similar polygons?

<p>all corresponding sides are proportional</p> Signup and view all the answers

What is the relationship between the perimeters of similar polygons?

<p>if 2 figures are similar, then perimeters are proportional to the scale factors between them</p> Signup and view all the answers

What do proportional parts of triangles refer to?

<p>non-parallel transversals that intersect parallel lines can be extended to form similar triangles</p> Signup and view all the answers

What does the side splitter theorem state?

<p>if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally AB/BC = AE/ED</p> Signup and view all the answers

What is the converse of the side splitter theorem?

<p>if the parts are proportionate, then the sides are parallel</p> Signup and view all the answers

What does the triangle midsegment theorem state?

<p>a midsegment of a triangle is parallel to one side of the triangle, and its length is 1/2 the length of that side</p> Signup and view all the answers

What is the proportional perimeter theorem?

<p>if F~G then a/x = b/y = c/z = a+b+c / x+y+z</p> Signup and view all the answers

What does the corresponding altitudes theorem state?

<p>if F~G then a/w = b/x = c/y = d/z</p> Signup and view all the answers

What is the corresponding angle bisector theorem?

<p>if F~G then a/w = b/x = c/y = d/z</p> Signup and view all the answers

What is the corresponding medians theorem?

<p>if F~G then a/w = b/x = c/y = d/z</p> Signup and view all the answers

What is the center of dilation?

<p>fixed point where dilation are performed</p> Signup and view all the answers

What is the scale factor of dilation?

<p>ratio of a length on the image to a corresponding length on the preimage</p> Signup and view all the answers

What does enlargement refer to in dilation?

<p>a dilation with a scale factor greater than 1</p> Signup and view all the answers

What does reduction refer to in dilation?

<p>a dilation with a scale factor between 0-1</p> Signup and view all the answers

How do you find the scale factor of enlargement?

<p>find distance between two points of each image, put the distance of smaller image over larger image</p> Signup and view all the answers

How do you find the scale factor of reduction?

<p>find distance between two points of each image, put the distance of larger image over distance of smaller image</p> Signup and view all the answers

What are reflections in geometry?

<p>the images are equal distances from the required segment or point</p> Signup and view all the answers

What is the reflection on the x-axis?

<p>multiply point in y coordinate by -1. (x,-y)</p> Signup and view all the answers

What is the reflection on the y-axis?

<p>multiply point in x coordinate by -1. (-x,y)</p> Signup and view all the answers

What are translations in geometry?

<p>to translate a point along a vector as a to the x coordinate and b to the y coordinate. (x+a, y+b)</p> Signup and view all the answers

What are rotations in geometry?

<p>90 rotation (-y,x), 180 rotation (-x,-y), 270 rotation (y,-x)</p> Signup and view all the answers

Study Notes

Ratios and Proportions

  • Ratio: A comparison of two quantities through division.
  • Proportion: An equation that asserts the equality between two ratios.
  • Extended Ratio: A ratio that compares three or more quantities.

Triangle Measurements

  • Triangle Ratios: For triangle sides in a ratio of 2:2:3 with a perimeter of 392, use 2x + 2x + 3x = 392 to find side lengths.
  • Perimeter Without Given Value: Set the ratios of triangle sides to equal 180 if perimeter is not provided.

Scale Models and Dilation

  • Scale Model: An object or drawing that maintains proportional lengths relative to the object it represents.
  • Dilation: A transformation that alters the size of an object without changing its shape.
  • Scale Factor: Represents the ratio of an image's length to the original object's length, e.g., 3:25 simplified to 1:100.

Similar Polygons

  • Similar Polygons: They share the same shape, though sizes may vary.
  • Rule #1: In similar polygons, all corresponding angles are congruent.
  • Rule #2: All corresponding sides within similar polygons remain proportional.

Perimeter and Triangle Theorems

  • Proportional Perimeters: If two figures are similar, their perimeters correspond to the scale factor.
  • Proportional Parts of Triangles: Non-parallel transversals intersecting parallel lines can create similar triangles.
  • Side Splitter Theorem: A line parallel to one side of a triangle divides the other two sides proportionally (AB/BC = AE/ED).
  • Converse of Side Splitter: If segments are proportional, the sides are parallel.
  • Triangle Midsegment Theorem: Midsegment is parallel to one triangle side and half its length.

Advanced Theorems

  • Proportional Perimeter Theorem: If figures F and G are similar, proportions of corresponding sides and perimeters are equal.
  • Corresponding Altitudes and Medians Theorems: Corresponding segments remain proportional for similar figures.

Dilation Properties

  • Center of Dilation: The fixed point used as a reference when performing dilations.
  • Types of Dilation:
    • Enlargement: Dilation with a scale factor greater than 1.
    • Reduction: Dilation with a scale factor between 0 and 1.

Finding Scale Factors

  • Scale Factor of Enlargement: Calculate the ratio of distances between two points on the smaller image to the larger image.
  • Scale Factor of Reduction: Compare distances from the larger image to the smaller image.

Transformations

  • Reflections: images are symmetrically opposite along a segment or point.
    • X-Axis Reflection: Invert the y-coordinate. Transformation results in (x, -y).
    • Y-Axis Reflection: Invert the x-coordinate. Transformation results in (-x, y).
  • Translations: Shifts a point by adding or subtracting from the coordinates. Represents movement along a vector (x + a, y + b).
  • Rotations:
    • 90°: (x, y) becomes (-y, x).
    • 180°: (x, y) becomes (-x, -y).
    • 270°: (x, y) becomes (y, -x).

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Prepare for your Geometry Chapter 7 test with these flashcards that cover essential concepts such as ratios, proportions, and extended ratios. Strengthen your understanding of how to work with triangles and their properties. Perfect for quick review or study sessions.

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