📐 Topic Summary
A 45-45-90 triangle is a special type of right triangle where the two acute angles are both 45 degrees. This means the two legs of the triangle are congruent (equal in length). The ratio of the sides in a 45-45-90 triangle is always $side : side : side\sqrt{2}$, where the legs are the 'side' and the hypotenuse is '$side\sqrt{2}$'. Knowing this ratio allows you to quickly find the lengths of the sides, even if you only know one side length!
This activity will test your understanding of 45-45-90 triangles, their properties, and how to apply the side ratios to solve for missing side lengths.
🔤 Part A: Vocabulary
Match the term to its definition:
| Term |
Definition |
| 1. Hypotenuse |
A. The side opposite the right angle in a right triangle. |
| 2. Leg |
B. One of the two shorter sides in a right triangle. |
| 3. Right Triangle |
C. A triangle with one angle measuring 90 degrees. |
| 4. Isosceles Triangle |
D. A triangle with two sides of equal length. |
| 5. 45-45-90 Triangle |
E. An isosceles right triangle with angles measuring 45°, 45°, and 90°. |
Match the numbers to the letters:
1. ___ 2. ___ 3. ___ 4. ___ 5. ___
✍️ Part B: Fill in the Blanks
Complete the paragraph using the words provided:
Words: congruent, hypotenuse, leg, $side\sqrt{2}$, 45
A 45-45-90 triangle has two angles that measure _____ degrees. The two ____ of the triangle are _____, meaning they have the same length. If the length of a leg is 'side', then the length of the _____ is _____.
🤔 Part C: Critical Thinking
Explain how knowing the length of the hypotenuse in a 45-45-90 triangle helps you find the length of each leg. Provide an example.
