8th Grade Module 3 Eureka Review

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$a^2 + b^2 = c^2$$ .

To find the missing side length in a right triangle, use the Pythagorean Theorem: $$a^2 + b^2 = c^2$$ . Rearrange the formula to solve for the missing side.

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of two corresponding sides of similar figures.

To determine the scale factor between two similar triangles, divide the length of a side of one triangle by the length of the corresponding side of the other triangle.

The formula to find the diagonal (d) of a rectangle with length (l) and width (w) is: $$d = \text{sqrt}(l^2 + w^2)$$ .

A right triangle is a triangle that has one angle measuring 90 degrees.

Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

In a right triangle, the longest side opposite the right angle is called the hypotenuse, while the other two sides are referred to as the legs.

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse, as stated by the Pythagorean Theorem.

The area (A) of a rectangle is calculated using the formula: $$A = l \times w$$ , where l is the length and w is the width.