π Topic Summary
Similar triangles are triangles that have the same shape but can be different sizes. Their corresponding angles are equal, and the ratio of their corresponding sides is constant. This constant ratio is called the scale factor. Proportions allow us to set up equations to find missing side lengths in similar triangles. Understanding these concepts unlocks a powerful tool for solving various geometric problems.
π Part A: Vocabulary
Match the following terms with their definitions:
- Term: Similar Triangles
- Term: Proportion
- Term: Corresponding Sides
- Term: Scale Factor
- Term: Congruent Angles
- Definition: Angles that have the same measure.
- Definition: The ratio between corresponding sides of similar figures.
- Definition: Triangles with the same shape but different sizes; corresponding angles are equal, and corresponding sides are in proportion.
- Definition: Sides that are in the same relative position in similar figures.
- Definition: An equation stating that two ratios are equal.
(Match the terms to the definitions, e.g., 1-C, 2-E, etc.)
βοΈ Part B: Fill in the Blanks
Similar triangles have the same _____, but can be different _____. Their corresponding _____ are equal, and the ratio of their corresponding _____ is constant. This constant ratio is called the _____ _____. We can use _____ to solve for missing side lengths.
(Possible answers: shape, sizes, angles, sides, scale factor, proportions)
π€ Part C: Critical Thinking
Explain, in your own words, how you can use similar triangles and proportions to estimate the height of a tall building or tree without physically measuring it. π³π’
