Question

Now that we have found the side lengths of two 45°-45°-90° triangles, we can observe a pattern in the lengths of sides of all 45°-45°-90° right triangles. Using the exact values written using square root expressions, fill in the table below.​

Answer 1

I hope you helped

Explanation:

To observe the pattern in the lengths of sides of all 45°-45°-90° right triangles, let's start by understanding the ratios between the sides.

In a 45°-45°-90° right triangle, the two legs are congruent (they have the same length) and the hypotenuse is equal to the length of one leg multiplied by the square root of 2 (√2).

Let's denote the length of one leg as "s". Then the other leg will also have a length of "s" and the hypotenuse will be "s√2".

Now, let's fill in the table below using the exact values written using square root expressions:

| Side Length | Ratio to Leg |

|-------------|--------------|

| s | 1 |

| s | 1 |

| s√2 | √2 |

In the table, "s" represents the length of one leg, which is the same as the length of the other leg. The ratio to leg column represents the ratio of each side length to the length of the leg.

So, for a 45°-45°-90° triangle, both legs have the same length "s" and the hypotenuse has a length of "s√2".

This pattern holds true for all 45°-45°-90° right triangles.