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Pythagorean Theorem
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PYTHAGOREAN THEOREM
What is Pythagorean Theorem?
Pythagorean Theorem or Pythagoras Theorem states, “In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides”. This can be expressed as c 2 = a 2 + b 2 ; where ‘c’ is the hypotenuse and ‘a’ and ‘b’ are the two legs of the triangle.
The Pythagorean theorem can be used to:
- To check if a triangle is right-angled
- To determine the speed of sound in the ocean by oceanographers
- To find the range and sound source by aerospace scientists and meteor
PYTHAGOREAN THEOREM WORKSHEETS
Pythagorean theorem- chart.
Identify Right Triangle - Customary units
- Worksheet #1
- Worksheet #2
- Worksheet #3
Identify Right Triangle - Metric units
Pythagorean Triples
Find the unknown length - Customary units
Find the unknown length -Metric units
Find the unknown length - Decimals - Customary units
Find the unknown length - Decimals - Metric units
Find the missing side length in shapes - Customary units
Find the missing side length in shapes - Metric units
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Home Math Worksheets > Geometry > Pythagorean Theorem
What is the Pythagorean Theorem? Pythagorean theorem describes the relation between the sides of a right-angled triangle. The Pythagorean formula is applied on a right-angled triangle and is used to determine the hypotenuse, base and the perpendicular of the triangle. The theorem states that: "In a right-angled triangle, the square of the hypotenuse side is equal to the squares of the perpendicular side and the base side." The hypotenuse is the longest side, and perpendicular is the side opposite to the hypotenuse side. Consider the triangle above, where a is the perpendicular side, b is the base side, and c is the hypotenuse. According to the definition of the Pythagorean theorem, the formula would be written as: c 2 = a 2 + b 2
When a triangle has a right-angle, we can use the sum of the squares of each leg of the triangle to find the squared value of the hypotenuse. It can be rearranged to find the length of any of the sides. The Pythagorean Theorem has so many different applications to everyday life that it is not even funny. The theorem allows us to completely understand a right-triangle system with ease. It is used measure distances that are applicable to everything from measuring a deck about to be constructed or building a skyscraper. Your students will use the theorem to solve for variables for given triangles. Some questions may be in the form of word problems. Students should be familiar with different types of triangles.
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Print pythagorean theorem worksheets, click the buttons to print each worksheet and associated answer key., introduction lesson.
This worksheet explains how to use the Pythagorean theorem. A sample problem is solved, and two practice problems are provided.
Introduction Worksheet
Students will use the theorem to solve these triangle based problems.
Practice Sheet
Example problem: Let the distance of the ship from its starting point be x km. We can draw a diagram of the ship's voyage on a set of axes, with the horizontal axis representing east and the vertical axis representing north. The ship is at the point P and it started at the origin. There is a right angle at A.
Review and Practice
Example problem: The foot of an Iron ladder is placed 30 feet from a wall. If the top of the ladder rests 50 feet up on the wall, how long is the ladder?
Quiz Part I
Students will demonstrate their proficiency in using the Pythagorean theorem to solve problems.
Quiz Part 2
These are the more visual based problems.
Introduction Check
Students will use the theorem to solve problems. Space is included for students to copy the correct answer when given.
Using the Theorem Lesson
The Pythagorean Theorem is a formula relating the lengths of the three sides of a right triangle. It is used when we know the length of two sides of a right triangle and we need to get the length of the third side.
Applying Lesson and Practice
This worksheet explains how to find the missing side length of a given triangle. A sample problem word problem is solved, and two practice problems are provided.
Active Worksheet
Students will use the theorem to solve problems involving right triangles.
Application Practice
For each right triangle provided, students will solve for the missing side length.
Set of Drills
Students will write the equation according to the Pythagorean theorem for each triangle and indicate whether or not the side measurements provided are correct. Eight problems are provided.
Application Warm Up
Students will find the diagonals of the squares. Three problems are provided.
Solve for the Missing Side Lesson
This worksheet explains how to solve for the missing side measurement of a triangle. A sample problem is solved, and two practice problems are provided.
Solve for the Missing Side Worksheet
Students will solve for the missing side measurement of a triangle.
Solve for the Missing Side Practice
Students will solve for x.
More Review Worksheet
The Pythagorean theorem is reviewed and we use it for our own benefit. A sample problem is solved.
Skill Practice
Missing side quiz.
Students will use the theorem to find the missing side measure.
Solve for the Missing Side Check
Students will solve for the missing side measurement of a triangle. Three problems are provided, and space is included for students to copy the correct answer when given.
Word Problem Lesson
This worksheet explains how to solve for the hypotenuse of a triangle. A sample problem is solved, and two practice problems are provided.
Word Problem Worksheet
If the sides of an isosceles right triangle are 4 inches long, approximate the length of the hypotenuse to the nearest whole number.
More Word Problem Practice
If the legs of an isosceles right triangle are 5 inches long, approximate the length of the hypotenuse to the nearest whole number.
Word Problem Review
We review with this problem: One leg of a triangular plate is 4 cm and other leg is of 3 cm. What is the hypotenuse?
Word Problem Review Sheet 2
Students will solve the word problems by using the Pythagorean Theorem.
Word Problem Quiz
Students will demonstrate their proficiency using the Pythagorean Theorem to solve word problems.
Quick Check
Example problem: Matt is flying a glider. He goes 5 km south and then 7 km west. How far is he from his starting point?
Solve for the Third Side Lesson
This worksheet explains how to use the Pythagorean theorem to determine the length of the third side of a triangle. A sample problem is solved.
Lesson and Practice
Given the measure of two sides of a triangle, this worksheet explains how to use the Pythagorean theorem to determine the length of the third side. A sample problem word problem is solved, and two practice problems are provided.
Third Side Worksheet
Students will use the theorem to solve for the length of the third side of each triangle.
Solving Sides Sides Practice
For each right triangle provided, students will solve for the length of the third side.
The Pythagorean Theorem Show the Skill
Determine the length of the third side of the right triangle.
Side Warm Up
Students will solve for the third side of each triangle. Three problems are provided.
Assorted Practice Problems
Students will solve an assortment of problems using the Pythagorean theorem.
Mixed Practice Worksheet
Students will use the theorem to solve assorted problems.
Practice Drill Set
Sample drill: In a right triangle, find the length of the side not given. Give an exact answer and approximation to three decimal places. b = 6, c = 10
Practice Skills Check
Students will demonstrate familiarity with the Pythagorean theorem.
Refresher Practice
Students will demonstrate proficiency with the Pythagorean theorem to solve for the length of the third side of each triangle.
Third Side Lesson
We walk you through how to solve this problem: A wired gate is 3 m wide and 1.6 m tall. It needs braces welded to it as shown in the picture. Find the length of the braces.
This worksheet explains how to use the Pythagorean theorem to find the area of an equilateral triangle. A sample problem word problem is solved, and two practice problems are provided.
Students will use the theorem to solve word problems.
Practice Worksheet
Here is an example: Gary takes a shortcut along the diagonal of a rectangular plot that is 25 cm wide and 17 cm long, instead of going along the sides. How much does that shorten his path?
A 13 feet ladder is placed on the wall of a house so that its lower end is 5 feet from the wall. At what height does the ladder touch the house?
Practical Worksheet
Find the perimeter of given lots.
IMAGES
VIDEO
COMMENTS
The Pythagorean theorem is used today in construction and various other professions and in numerous day-to-day activities. In construction, this theorem is one of the methods builders use to lay the foundation for the corners of a building.
The Pythagorean theorem forms the basis of trigonometry and, when applied to arithmetic, it connects the fields of algebra and geometry, according to Mathematica.ludibunda.ch. The uses of this theorem are almost limitless.
Architects use the Pythagorean theorem, which is expressed by the equation: a2 + b2 = c2, in designing and computing the measurements of building structures and bridges. One example involves roof design.
Use the Pythagorean Theorem to solve for x.
Create your own worksheets like this one with Infinite Pre-Algebra.
Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth. Sheet 1. Pythagorean Theorem.
Formulated in the 6th Century BC by Greek Philosopher and mathematician Pythagoras of Samos, Pythagorean Theorem is a mathematic equation used for a variety of
Create your own worksheets like this one with Infinite Pre-Algebra.
PYTHAGOREAN THEOREM. WORKSHEET. For each triangle find the missing length. Round your answer to the nearest tenth. Then find the area and the perimeter.
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Find the perimeter of each figure. Round your answer to the nearest tenth. Did you use the Pythagorean Theorem? If so, explain. a. Right triangle.
Pythagorean theorem or Pythagoras theorem is the sum of two sides of a triangle is equal to the square of the hypotenuse.
Take the Schoology Quiz (Level 2: Pythagorean Theorem) ... Use Pythagorean Theorem to find missing hypotenuse on right triangle.
The Pythagorean formula is applied on a right-angled triangle and is used to determine the hypotenuse, base and the perpendicular of the triangle. The theorem