# Standard 1: Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles. Export Print
General Information
Number: MA.8.GR.1
Title: Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.8.GR.1.AP.1
Find the hypotenuse of a two-dimensional right triangle using the Pythagorean Theorem.
MA.8.GR.1.AP.2
Given the Pythagorean Theorem, determine lengths/distances between two points in a coordinate system by forming right triangles, with natural number side lengths.
MA.8.GR.1.AP.3a
Measure the sides of triangles to establish facts about the Triangle Inequality Theorem (i.e., the sum of two side lengths is greater than the third side).
MA.8.GR.1.AP.3b
Substitute the side lengths of a given figure into the Pythagorean Theorem to determine if a right triangle can be formed.
MA.8.GR.1.AP.4
Identify supplementary, complementary, vertical or adjacent angle relationships.
MA.8.GR.1.AP.5
Given an image, solve simple problems involving the relationships of interior and exterior angles of a triangle.
MA.8.GR.1.AP.6
Use tools to calculate the sum of the interior angles of regular polygons when given the formula.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Formative Assessments

Distance Between Two Points:

Students are asked to find the distance between two points in the coordinate plane.

Type: Formative Assessment

Three Dimensional Diagonal:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

Pythagorean Squares:

Students are asked to explain how a pair of figures demonstrates the Pythagorean Theorem and its converse.

Type: Formative Assessment

New Television:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

Justifying the Exterior Angle of a Triangle Theorem:

Students are asked to apply the Exterior Angle of a Triangle Theorem and provide an informal justification.

Type: Formative Assessment

How Far to School:

Students are asked to determine the length of a side of a right triangle in a real-world problem.

Type: Formative Assessment

Students are asked use knowledge of angle relationships to write and solve an equation to determine an unknown angle measure.

Type: Formative Assessment

Sides of Triangles:

Students are asked to determine if given lengths will determine a triangle.

Type: Formative Assessment

Drawing Triangles SSS:

Students are asked to draw a triangle with given side lengths, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

Straight Angles:

Students are asked to write and solve equations to determine unknown angle measures in supplementary angle relationships.

Type: Formative Assessment

Solve for the Angle:

Students are asked to write and solve equations to determine unknown angle measures in supplementary and complementary angle pairs.

Type: Formative Assessment

Find the Angle Measure:

Students are asked to use knowledge of angle relationships to write and solve equations to determine unknown angle measures.

Type: Formative Assessment

Distance on the Coordinate Plane:

Students are asked to find the distance between two points in the coordinate plane.

Type: Formative Assessment

Coordinate Plane Triangle:

Students are asked to determine the lengths of the sides of a right triangle in the coordinate plane given the coordinates of its vertices.

Type: Formative Assessment

Calculate Triangle Sides:

Students are asked to determine the length of each side of a right triangle in the coordinate plane given the coordinates of its vertices.

Type: Formative Assessment

## Lesson Plans

Shape It Up:

Students will derive the formula for the sum of the interior angles of a polygon by drawing diagonals and applying the Triangle Sum Theorem. The measure of each interior angle of a regular polygon is also determined.

Type: Lesson Plan

Just Plane Ol' Area!:

Students will construct various figures on coordinate planes and calculate the perimeter and area. Use of the Pythagorean theorem will be required.

Type: Lesson Plan

Triangles: Finding Interior Angle Measures:

The lesson begins with a hands-on activity and then an experiment with a GeoGebra-based computer model to discover the Triangle Angle Sum Theorem. The students write and solve equations to find missing angle measures in a variety of examples.

Type: Lesson Plan

Pythagoras - You Clever Dog:

This lesson starts with an introduction of the Pythagorean Theorem. It introduces vocabulary, formulas and concepts related to right triangles and the use of the Pythagorean Theorem in the real world. Students will learn the basics through real world application.

Type: Lesson Plan

## Original Student Tutorials

Pythagorean Theorem: Part 3:

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 2:

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 1:

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Playground Angles Part 1:

Explore complementary and supplementary angles around the playground with Jacob in this interactive tutorial.

This is Part 1 in a two-part series. Click HERE to open Playground Angles: Part 2.

Type: Original Student Tutorial

Playground Angles: Part 2:

Help Jacob write and solve equations to find missing angle measures based on the relationship between angles that sum to 90 degrees and 180 degrees in this playground-themed, interactive tutorial.

This is Part 2 in a two-part series. Click HERE to open Playground Angles: Part 1.

Type: Original Student Tutorial

Applying the Pythagorean Theorem to Solve Mathematical and Real-World problems:

Apply the Pythagorean Theorem to solve mathematical and real-rorld problems in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

What's the Distance from Here to the Middle of Nowhere?:

Find out how math and technology can help you (try to) get away from civilization.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Type: Perspectives Video: Teaching Idea

## Text Resource

Pythagoras Explained:

This informational text resource is intended to support reading in the content area. The text describes a method for predicting the win-loss record for baseball teams based on runs scored and runs allowed, using the "Pythagorean Expectation" formula invented by Bill James. The text goes on to show the relationship of the prediction formula to the Pythagorean theorem, pointing out a very cool application of the theorem to the world of sports.

Type: Text Resource

## Tutorials

Finding Missing Angle Measures:

In this video, we find missing angle measures from a variety of examples.

Type: Tutorial

Finding the Measure of Complementary Angles:

The video will use algebra to find the measure of two angles whose sum equals 90 degrees, better known as complementary angles.

Type: Tutorial

Find Measure of Complementary Angles:

Watch as we use algebra to find the measure of two complementary angles.

Type: Tutorial

Find Measure of Supplementary Angles:

Watch as we use algebra to find the measure of supplementary angles, whose sum is 180 degrees.

Type: Tutorial

Find Measure of Vertical Angles:

This video uses knowledge of vertical angles to solve for the variable and the angle measures.

Type: Tutorial

Introduction to Vertical Angles:

This video uses facts about supplementary and adjacent angles to introduce vertical angles.

Type: Tutorial

Find Measure of Angles in a Word Problem:

This video demonstrates solving a word problem involving angle measures.

Type: Tutorial

Construct a Right Isosceles Triangle:

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

Construct a Triangle with Given Side Lengths:

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

Complementary and Supplementary Angles:

The video will demonstrate the difference between supplementary angles and complementary angles, by using the given measurements of angles.

Type: Tutorial

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Original Student Tutorials

Pythagorean Theorem: Part 3:

Use the Pythagorean Theorem to find the legs of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 2:

Use the Pythagorean Theorem to find the hypotenuse of a right triangle in mathematical and real worlds contexts in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Pythagorean Theorem: Part 1:

Learn what the Pythagorean Theorem and its converse mean, and what Pythagorean Triples are in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Type: Original Student Tutorial

Playground Angles Part 1:

Explore complementary and supplementary angles around the playground with Jacob in this interactive tutorial.

This is Part 1 in a two-part series. Click HERE to open Playground Angles: Part 2.

Type: Original Student Tutorial

Playground Angles: Part 2:

Help Jacob write and solve equations to find missing angle measures based on the relationship between angles that sum to 90 degrees and 180 degrees in this playground-themed, interactive tutorial.

This is Part 2 in a two-part series. Click HERE to open Playground Angles: Part 1.

Type: Original Student Tutorial

Applying the Pythagorean Theorem to Solve Mathematical and Real-World problems:

Apply the Pythagorean Theorem to solve mathematical and real-rorld problems in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

What's the Distance from Here to the Middle of Nowhere?:

Find out how math and technology can help you (try to) get away from civilization.

Type: Perspectives Video: Professional/Enthusiast

## Tutorials

Finding Missing Angle Measures:

In this video, we find missing angle measures from a variety of examples.

Type: Tutorial

Finding the Measure of Complementary Angles:

The video will use algebra to find the measure of two angles whose sum equals 90 degrees, better known as complementary angles.

Type: Tutorial

Find Measure of Complementary Angles:

Watch as we use algebra to find the measure of two complementary angles.

Type: Tutorial

Find Measure of Supplementary Angles:

Watch as we use algebra to find the measure of supplementary angles, whose sum is 180 degrees.

Type: Tutorial

Find Measure of Vertical Angles:

This video uses knowledge of vertical angles to solve for the variable and the angle measures.

Type: Tutorial

Introduction to Vertical Angles:

This video uses facts about supplementary and adjacent angles to introduce vertical angles.

Type: Tutorial

Find Measure of Angles in a Word Problem:

This video demonstrates solving a word problem involving angle measures.

Type: Tutorial

Construct a Right Isosceles Triangle:

This video discusses constructing a right isosceles triangle with given constraints and deciding if the triangle is unique.

Type: Tutorial

Construct a Triangle with Given Side Lengths:

This video demonstrates drawing a triangle when the side lengths are given.

Type: Tutorial

Complementary and Supplementary Angles:

The video will demonstrate the difference between supplementary angles and complementary angles, by using the given measurements of angles.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

## Perspectives Video: Expert

Measuring a Grid for Underwater Archeology:

Don't be a square! Learn about how even grids help archaeologists track provenience!