📚 Topic Summary
When an altitude is drawn from the right angle of a right triangle to the hypotenuse, it creates two smaller triangles. These smaller triangles are similar to each other and to the original, larger triangle. Understanding this relationship allows us to solve various geometric problems involving proportions and side lengths. This activity will help you practice identifying these similar triangles.
📐 Part A: Vocabulary
Match the term with its correct definition.
| Term |
Definition |
| 1. Altitude |
A. Triangles with the same shape but different sizes. |
| 2. Right Triangle |
B. The side opposite the right angle in a right triangle. |
| 3. Hypotenuse |
C. A line segment from a vertex perpendicular to the opposite side. |
| 4. Similarity |
D. A triangle containing one 90-degree angle. |
| 5. Similar Triangles |
E. The condition where two figures have the same shape, angles are equal, and sides are in proportion. |
Answer Key: 1-C, 2-D, 3-B, 4-E, 5-A
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: similar, altitude, hypotenuse, right triangle, proportions.
When an ________ is drawn from the right angle of a ________ to the ________, it forms two ________ triangles. Because these triangles are similar, their corresponding sides are in ________.
Answer: altitude, right triangle, hypotenuse, similar, proportions.
🤔 Part C: Critical Thinking
Explain in your own words why the triangles formed by an altitude in a right triangle are always similar. What geometric principles are at play here?
