📐Topic Summary
Similarity in geometry means that two shapes have the same angles and their sides are in proportion. When dealing with similar triangles or other polygons, you can use this property to find the lengths of unknown sides. By setting up ratios of corresponding sides, you can create proportions and solve for the missing lengths using cross-multiplication or other algebraic techniques. Knowing how to apply similarity is super handy for solving real-world problems, like figuring out heights or distances!
🔤 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Similar Polygons |
a. A statement that two ratios are equal. |
| 2. Proportion |
b. Polygons that have the same shape but different sizes. |
| 3. Corresponding Sides |
c. The ratio of any length in a figure to its corresponding length in a similar figure. |
| 4. Scale Factor |
d. Sides in the same relative position in similar polygons. |
| 5. Cross Products |
e. The result of multiplying the numerator of one fraction by the denominator of another. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: similar, proportional, corresponding, ratios, scale factor.
If two triangles are ________, their ________ angles are congruent, and their ________ sides are ________. You can find missing side lengths by setting up equal ________ and solving. The ________ is the ratio between the side lengths of the two triangles.
🤔 Part C: Critical Thinking
Imagine you're using similar triangles to estimate the height of a tree. Explain the steps you would take to measure the necessary distances and set up the proportion to find the tree's height. What potential sources of error might affect the accuracy of your estimate?
