Geometry Chapter 7 Test Flashcards

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).

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.