๐ Topic Summary
Indirect measurement uses the properties of similar triangles to find lengths that are difficult or impossible to measure directly. By setting up proportions based on corresponding sides of similar triangles, we can solve for unknown distances. This technique is often used to determine the heights of buildings, trees, or other tall objects by comparing their shadows to the shadow of a known object.
๐ Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Similar Triangles |
A. The ratio of two corresponding sides in similar triangles. |
| 2. Proportion |
B. A statement that two ratios are equal. |
| 3. Corresponding Sides |
C. Triangles that have the same shape but different sizes. |
| 4. Scale Factor |
D. Sides in similar triangles that are in the same relative position. |
| 5. Indirect Measurement |
E. A technique using proportions to find measurements that are difficult to measure directly. |
Match the correct term to the definition. Answers will appear at the end of this worksheet!
โ๏ธ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: similar, corresponding, proportion, height, shadow.
Indirect measurement often involves using __________ triangles. By comparing the __________ of an object to the __________ of a known object, we can set up a __________ to determine the unknown __________. The key is to identify __________ sides and set up the ratios correctly.
๐ค Part C: Critical Thinking
Explain how you could use indirect measurement to estimate the height of a tall tree in your backyard. What materials would you need, and what measurements would you take?