Math 8B unit 2 triangle lesson 6 distance and the phythagorean theorem

Answer 1

In Lesson 6 of Unit 2- Triangles, we will be discussing the concept of distance and exploring the Pythagorean Theorem.

Distance can be defined as the measure between two points in space. In a two-dimensional coordinate plane, distance can be found using the formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Here, (x1, y1) and (x2, y2) represent the coordinates of the two endpoints or points.

The Pythagorean Theorem is a mathematical formula that relates the lengths of the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In mathematical terms, the Pythagorean Theorem can be represented as:

a^2 + b^2 = c^2

Here, 'a' and 'b' represent the lengths of the two shorter sides (legs) of the right triangle, and 'c' represents the length of the hypotenuse.

The Pythagorean Theorem can be used in various situations, such as finding the missing side lengths of right triangles, determining if a triangle is a right triangle, and finding the distance between two points in a two-dimensional plane.

In this lesson, we will learn how to apply the Pythagorean Theorem to solve various problems involving distances and right triangles. We will also discuss the importance and applications of the Pythagorean Theorem in real-life scenarios such as architecture, engineering, and navigation.

Overall, Lesson 6 of Unit 2 will focus on understanding distance and the Pythagorean Theorem and using them to solve problems pertaining to right triangles.