**Title:** Distance "The Pythagoras Way"

**Description:**
In this lesson, the teacher will demonstrate how to use the Pythagorean Theorem to find distance between two points in the coordinate system. In the coordinate plane, the difference in the x- and y-values will determine the numbers to calculate the distance. This lesson will use online graphing tools as well as graph paper to plot the points. This lesson can also be used to show the relationship between the distance formula and the Pythagorean Theorem.
This lesson results from the ALEX Resource Gap Project.
**Standard(s): **

[MA2015] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8]

**Subject:**Mathematics (8)

**Title:**Distance "The Pythagoras Way"

**Description:**In this lesson, the teacher will demonstrate how to use the Pythagorean Theorem to find distance between two points in the coordinate system. In the coordinate plane, the difference in the x- and y-values will determine the numbers to calculate the distance. This lesson will use online graphing tools as well as graph paper to plot the points. This lesson can also be used to show the relationship between the distance formula and the Pythagorean Theorem. This lesson results from the ALEX Resource Gap Project.

**Title:** Proofs into Practice: The Pythagorean Theorem in the Real World

**Description:**
The introduction of this lesson has students verifying the famous Pythagorean Theorem with a hands-on proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two real-life applicataions to explore, using the Pythagorean Theorem.
**Standard(s): **

[MA2015] GEO (9-12) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

**Subject:**Mathematics (8 - 12)

**Title:**Proofs into Practice: The Pythagorean Theorem in the Real World

**Description:**The introduction of this lesson has students verifying the famous Pythagorean Theorem with a hands-on proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two real-life applicataions to explore, using the Pythagorean Theorem.

**Title:** Understanding the Pythagorean Relationship Using Interactive Figures

**Description:**
The Pythagorean relationship, a2 + b2 = c2 (where a and b are the lengths of the legs of a right triangle and c is the hypotenuse), can be demonstrated in many ways, including with visual 'proofs' that require little or no symbolism or explanation. The activity in this example from Illuminations presents one dynamic version of a demonstration of this relationship. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
**Standard(s): **

[MA2015] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8]

**Subject:**Mathematics

**Title:**Understanding the Pythagorean Relationship Using Interactive Figures

**Description:**The Pythagorean relationship, a2 + b2 = c2 (where a and b are the lengths of the legs of a right triangle and c is the hypotenuse), can be demonstrated in many ways, including with visual 'proofs' that require little or no symbolism or explanation. The activity in this example from Illuminations presents one dynamic version of a demonstration of this relationship. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Proof Without Words: Pythagorean Theorem

**Description:**
In this student interactive, from Illuminations, students watch a dynamic, geometric '' proof without words'' of the Pythagorean Theorem. By clicking on a button, students can see the theorem in action; they are then challenged to explain the proof.
**Standard(s): **

[MA2015] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8]

**Subject:**Mathematics

**Title:**Proof Without Words: Pythagorean Theorem

**Description:**In this student interactive, from Illuminations, students watch a dynamic, geometric '' proof without words'' of the Pythagorean Theorem. By clicking on a button, students can see the theorem in action; they are then challenged to explain the proof.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8