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Pythagorean Theorem Worksheets

These printable worksheets have exercises on finding the leg and hypotenuse of a right triangle using the Pythagorean theorem. Pythagorean triple charts with exercises are provided here. Word problems on real time application are available. Moreover, descriptive charts on the application of the theorem in different shapes are included. These handouts are ideal for 7th grade, 8th grade, and high school students. Kick into gear with our free Pythagorean theorem worksheets!

Identifying Right Triangles

Identifying Right Triangles

Apply Pythagorean theorem to identify whether the given triangle is a right triangle. Each printable worksheet consists of six problems.

exercise 1

Pythagorean Theorem Chart

These descriptive charts explain the Pythagorean theorem with an illustration. These pdfs emphasize the relation of the theorem derived as an equation.

chart 1

Pythagorean Triple

A set of three numbers is given in each problem. Grade 7 and grade 8 students need to apply the theorem and identify whether the set of numbers forms a Pythagorean triple.

worksheet 1

Pythagorean Triple Chart

This section comprises of Pythagorean triple sets up to 100. Besides, Pythagorean triple formulas with examples are provided in the charts.

Unknown Side of a Right Triangle

Unknown Side of a Right Triangle

Apply Pythagorean theorem to find the unknown side of the right triangle. Round the answer to the nearest tenth.

practice 1

Unknown Length: Shapes

Apply the Pythagorean theorem to find the unknown length of each shape in these printable worksheets. Round the answer to the nearest tenth.

pdf 1

Word Problems | Level 1

Brighten your math class with this bundle of real-life word problems based on the Pythagorean Theorem. Solve each word problem by finding the missing hypotenuse of the right triangle and rounding off the answer to the nearest tenth.

printable 1

Word Problems | Level 2

Presenting word problems with clear illustrations, these pdf worksheets require high school students to plug in the known values into the equation form of the Pythagorean Theorem and figure out the unknown side of the right triangle.

Related Worksheets

» Pythagorean Inequality Theorem

» Triangle

» Triangle Inequality Theorem

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  • Unit 5 - Pythagorean Theorem

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Unit 5 - Pythagorean Theorem

Listed below are the lessons for unit 5.  if we have covered a lesson, answer keys will be linked.

   

STUDY GUIDES & THEIR ANSWER KEYS

CCSS: 8.EE.2, 8.G.6, 8.G.7 and 8.G.8

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Geometry Worksheets to Practice Using the Pythagorean Theorem

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The Pythagorean Theorem is believed to have been was discovered on a Babylonian tablet circa 1900-1600 B.C.

The  Pythagorean Theorem  relates to the three sides of a right triangle . It states that c2=a2+b2, C is the side that is opposite the right angle which is referred to as the hypotenuse. A and b are the sides that are adjacent to the right angle.

The theorem simply stated is: the  sum of the areas  of two small squares equals the area of the large one.

You will find that the Pythagorean Theorem is used on any formula that will square a number. It's used to determine the shortest path when crossing through a park or recreation center or field. The theorem can be used by painters or construction workers, think about the angle of the ladder against a tall building for instance. There are many word problems in the classic math textbooks that require the use of the Pythagorean Theorem.

History Behind Pythagorean's Theorem

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Hippasus of Metapontum was born in the 5th Century BC. It is believed that he proved the existence of irrational numbers at a time when the Pythagorean belief was that whole numbers and their ratios could describe anything that was geometric. Not only that, they didn't believe there was a need for any other numbers .

The Pythagoreans were a strict society and all discoveries that happened had to be directly credited to them, not the individual responsible for the discovery. The Pythagoreans were very secretive and did not want their discoveries to 'get out' so to speak. They considered whole numbers to be their rulers and that all quantities could be explained by whole numbers and their ratios. An event would happen that would change the very core of their beliefs. Along came Pythagorean Hippasus who discovered that the diagonal of a square whose side was one unit could not be expressed as a whole number or a ratio.

What Is the Hypotenuse?

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Simply put, the hypotenuse of a right triangle is the side opposite the right angle. It is sometimes referred to by students as the long side of the triangle. The other two sides are referred to as the legs of the triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. 

The hypotenuse is the side of the triangle where C is. Always understand that the Pythagorean Theorem relates the areas of squares on the sides of the right triangle

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pythagorean theorem homework 5 answer key

Right Triangles & Pythagorean Theorem (Lesson 4.5)

Unit 1: reasoning in geometry, day 1: creating definitions, day 2: inductive reasoning, day 3: conditional statements, day 4: quiz 1.1 to 1.3, day 5: what is deductive reasoning, day 6: using deductive reasoning, day 7: visual reasoning, day 8: unit 1 review, day 9: unit 1 test, unit 2: building blocks of geometry, day 1: points, lines, segments, and rays, day 2: coordinate connection: midpoint, day 3: naming and classifying angles, day 4: vertical angles and linear pairs, day 5: quiz 2.1 to 2.4, day 6: angles on parallel lines, day 7: coordinate connection: parallel vs. perpendicular, day 8: coordinate connection: parallel vs. perpendicular, day 9: quiz 2.5 to 2.6, day 10: unit 2 review, day 11: unit 2 test, unit 3: congruence transformations, day 1: introduction to transformations, day 2: translations, day 3: reflections, day 4: rotations, day 5: quiz 3.1 to 3.4, day 6: compositions of transformations, day 7: compositions of transformations, day 8: definition of congruence, day 9: coordinate connection: transformations of equations, day 10: quiz 3.5 to 3.7, day 11: unit 3 review, day 12: unit 3 test, unit 4: triangles and proof, day 1: what makes a triangle, day 2: triangle properties, day 3: proving the exterior angle conjecture, day 4: angle side relationships in triangles, day 5: right triangles & pythagorean theorem, day 6: coordinate connection: distance, day 7: review 4.1-4.6, day 8: quiz 4.1to 4.6, day 9: establishing congruent parts in triangles, day 10: triangle congruence shortcuts, day 11: more triangle congruence shortcuts, day 12: more triangle congruence shortcuts, day 13: triangle congruence proofs, day 14: triangle congruence proofs, day 15: quiz 4.7 to 4.10, day 16: unit 4 review, day 17: unit 4 test, unit 5: quadrilaterals and other polygons, day 1: quadrilateral hierarchy, day 2: proving parallelogram properties, day 3: properties of special parallelograms, day 4: coordinate connection: quadrilaterals on the plane, day 5: review 5.1-5.4, day 6: quiz 5.1 to 5.4, day 7: areas of quadrilaterals, day 8: polygon interior and exterior angle sums, day 9: regular polygons and their areas, day 10: quiz 5.5 to 5.7, day 11: unit 5 review, day 12: unit 5 test, unit 6: similarity, day 1: dilations, scale factor, and similarity, day 2: coordinate connection: dilations on the plane, day 3: proving similar figures, day 4: quiz 6.1 to 6.3, day 5: triangle similarity shortcuts, day 6: proportional segments between parallel lines, day 7: area and perimeter of similar figures, day 8: quiz 6.4 to 6.6, day 9: unit 6 review, day 10: unit 6 test, unit 7: special right triangles & trigonometry, day 1: 45˚, 45˚, 90˚ triangles, day 2: 30˚, 60˚, 90˚ triangles, day 3: trigonometric ratios, day 4: using trig ratios to solve for missing sides, day 5: review 7.1-7.4, day 6: quiz 7.1 to 7.4, day 7: inverse trig ratios, day 8: applications of trigonometry, day 9: quiz 7.5 to 7.6, day 10: unit 7 review, day 11: unit 7 test, unit 8: circles, day 1: coordinate connection: equation of a circle, day 2: circle vocabulary, day 3: tangents to circles, day 4: chords and arcs, day 5: perpendicular bisectors of chords, day 6: inscribed angles and quadrilaterals, day 7: review 8.1-8.6, day 8: quiz 8.1 to 8.6, day 9: area and circumference of a circle, day 10: area of a sector, day 11: arc length, day 12: quiz 8.7 to 8.9, day 13: unit 8 review, day 14: unit 8 test, unit 9: surface area and volume, day 1: introducing volume with prisms and cylinders, day 2: surface area and volume of prisms and cylinders, day 3: volume of pyramids and cones, day 4: surface area of pyramids and cones, day 5: review 9.1-9.4, day 6: quiz 9.1 to 9.4, day 7: volume of spheres, day 8: surface area of spheres, day 9: problem solving with volume, day 10: volume of similar solids, day 11: quiz 9.5 to 9.8, day 12: unit 9 review, day 13: unit 9 test, unit 10: statistics and probability, day 1: categorical data and displays, day 2: measures of center for quantitative data, day 3: measures of spread for quantitative data, day 4: quiz review (10.1 to 10.3), day 5: quiz 10.1 to 10.3, day 6: scatterplots and line of best fit, day 7: predictions and residuals, day 8: models for nonlinear data, day 9: quiz review (10.4 to 10.6), day 10: quiz 10.4 to 10.6, day 11: probability models and rules, day 12: probability using two-way tables, day 13: probability using tree diagrams, day 14: quiz review (10.7 to 10.9), day 15: quiz 10.7 to 10.9, day 16: random sampling, day 17: margin of error, day 18: observational studies and experiments, day 19: random sample and random assignment, day 20: quiz review (10.10 to 10.13), day 21: quiz 10.10 to 10.13, learning targets.

Understand that the Pythagorean Theorem gives the relationship between the areas of the squares made from the sides of a right triangle.

Prove the Pythagorean Theorem.

Solve for missing sides in a right triangle.

Determine if a triangle is right, acute, or obtuse based on its side lengths.

Activity: A Pythagorean Puzzle

Lesson handouts, media locked, additional media.

pythagorean theorem homework 5 answer key

Our Teaching Philosophy:

Experience first, formalize later (effl), experience first.

To prepare for today's lesson, print the Shape Materials file found under "Additional Media" so that each page of the document is in a different color, preferably on cardstock. Each group will need one set of papers. Students will also need scissors and perhaps rulers.

Each group member will start with one of the four papers and cut out the shape(s) according to the instructions, then pass the paper to their group member. Set a timer for students so this part does not take longer than 5-8 minutes.

Next, students will work in groups on questions 1-6 in the activity using the shapes they just cut out. The goal is for students to understand that when we square a side length, we're referring to the area of a literal square coming off that side. The sum of the two smaller squares will always equal the large square. Most students can state "a^2 + b^2 =c^2" even before Geometry class, but few of them know what this means visually.

In the debrief, focus on question 6, where we label the lengths using variable names and then reason through equivalent areas. This is a great tie in to important Algebra standards about squaring binomials and the distributive property! Once you've established that the two figures have the same overall area, remove one triangle from both configurations at the same time. Ask students: "Do they still have the same area? Why?" This not only reinforces ideas about equivalence, but also helps students think about proof! Continue with these two questions for all 4 triangles, removing one at time. This may seem tedious, but it is worth it for students to see that at the end a^2 +b^2 is equal to c^2!

In questions 7 and 8, students consider obtuse and acute triangles. Note that only the angle is changing, not the lengths of the two "legs". In the case of an acute triangle, there is not necessarily a "large square", but we use this language to refer to the square across from the original right angle. Use this Geogebra applet for students to visualize how the areas of the squares are changing.

Formalize Later

While we do use the variables a, b, and c, remind students that these are arbitrary choices. "c" is not code for hypotenuse, and they must re-assess in every question which sides are the legs and which is the hypotenuse. On homework and assessment questions, we like to label the side lengths as d, o, and g or some other three letter word and have students write an equation relating the three sides. We know some teachers prefer leg^2 +leg^2=hyptoenuse^2 for the more generalized version of the Pythagorean theorem, but this language does not translate as well to the criteria for obtuse and acute triangles, where there are no legs or hypotenuse.

When you assess students on the Pythagorean theorem, make sure you write some questions that relate back to the geometric representation of the squares. Otherwise, students will resort back very quickly to mimicking the procedure for finding a missing side algebraically. Question 1 in the Check Your Understanding is one way you can do this.

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IMAGES

  1. Lesson 5 Extra Practice The Pythagorean Theorem Answer Key

    pythagorean theorem homework 5 answer key

  2. Pythagorean Theorem Worksheet With Answers

    pythagorean theorem homework 5 answer key

  3. Lesson 6 Homework Practice Use the Pythagorean Theorem Form

    pythagorean theorem homework 5 answer key

  4. Answer Key Pythagorean Theorem Worksheet Answers

    pythagorean theorem homework 5 answer key

  5. Pythagorean Theorem Worksheet With Answers

    pythagorean theorem homework 5 answer key

  6. Pythagorean Theorem Study Guide Answer Key

    pythagorean theorem homework 5 answer key

VIDEO

  1. Converse of the Pythagorean Theorem

  2. Pythagorean Theorem: Practice

  3. The Pythagorean theorem || @ecademy62721

  4. The Pythagorean Theorem with Variables (Algebra I)

  5. THE PYTHAGOREAN THEOREM#shorts#math

  6. Visual proof of pythagorean theorem || Pythagoras theorem practical

COMMENTS

  1. 48 Pythagorean Theorem Worksheet with Answers [Word + PDF]

    A simple equation, Pythagorean Theorem states that the square of the hypotenuse (the side opposite to the right angle triangle) is equal to the sum of the other two sides. Following is how the Pythagorean equation is written: a²+b²=c²

  2. PDF NAME DATE PERIOD Lesson 5 Skills Practice

    The Pythagorean Theorem Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. in. 8 in. 7 in. 72 + 82 = c2; 10.6 in. 2. 10 m a m 3. b cm 5 m 3 cm 11 cm a2 + 52 = 102; 8.7 m 4. 18 ft 15 ft 5. 24 yd c ft 182 + 152 = c2; 23.4 ft

  3. Pythagorean Theorem Practice Problems With Answers

    Let's get started! Here's the Pythagorean Theorem formula for your quick reference. Note: drawings not to scale Problem 1: Find the value of [latex]x [/latex] in the right triangle. Answer Problem 2: Find the value of [latex]x [/latex] in the right triangle. Answer Problem 3: Find the value of [latex]x [/latex] in the right triangle. Answer

  4. Pythagorean theorem

    The Pythagorean theorem describes a special relationship between the sides of a right triangle. Even the ancients knew of this relationship. In this topic, we'll figure out how to use the Pythagorean theorem and prove why it works. Pythagorean theorem Learn Intro to the Pythagorean theorem Pythagorean theorem example

  5. Pythagorean Theorem Worksheets

    Unknown Side of a Right Triangle Apply Pythagorean theorem to find the unknown side of the right triangle. Round the answer to the nearest tenth. Unknown Length: Shapes Apply the Pythagorean theorem to find the unknown length of each shape in these printable worksheets. Round the answer to the nearest tenth. Word Problems | Level 1

  6. Hanley, Joe / Unit 5

    Unit 5 starts off our return from Winter Break with students beginning their investigations into Perfect Squares and Perfect Cubes. Students will them move onto the Pythagorean Theorem, using the theorem to find the missing length of the Hypotenuse and the missing length of a leg of a right triangle. Included in those lessons will be using the ...

  7. Pythagorean theorem word problems (practice)

    Pythagorean theorem word problems. Google Classroom. You might need: Calculator. Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner.

  8. Worksheets to Practice Pythagorean Theorem Problems

    The Pythagorean Theorem relates to the three sides of a right triangle. It states that c2=a2+b2, C is the side that is opposite the right angle which is referred to as the hypotenuse. A and b are the sides that are adjacent to the right angle. The theorem simply stated is: the sum of the areas of two small squares equals the area of the large one.

  9. 3D Applications of the Pythagorean Theorem

    9.5 - 3D APPLICATIONS OF THE PYTHAGOREAN THEOREM - Video Notes. Pythagorean theorem in 3D - Khan Academy. Proudly powered by Weebly. Home Functions Functions Vocabulary Identifying Functions Function Videos Comparing Functions Common Core Standards Linear vs. Non-Linear Functions ...

  10. 5-5 The Pythagorean Theorem

    5-5 The Pythagorean Theorem. Essential Question: How can algebraic concepts be applied to Geometry? Objective: use the Pythagorean Theorem. Vocabulary: ... 5-5 Extra practice pg 417.pdf (646k) [email protected], Jun 16, 2014, 5:05 PM. v.1. ď. ĉ. 5-5 Homework_Practice_The_Pythagorean_Theorem.docx (75k) [email protected], Apr 2 ...

  11. PDF THE PYTHAGOREAN THEOREM

    The Pythagorean Theorem can be used to find the distance between two points, as shown below. Examples 1. Use the Pythagorean Theorem to find the distance between the points A(2, 3) and B(7, 10). Write your answer in simplest radical form. 2. Use the Pythagorean Theorem to find the distance between the points A(-3, 4) and B(5, -6).

  12. Practicing Pythagorean Theorem Worksheets

    Detailed Description for All Pythagorean Theorem Worksheets. This Pythagorean Theorem Problems Worksheet will produce problems for practicing solving the lengths of right triangles. You may choose the type of numbers and the sides of the triangle. This worksheet is a great resources for the 6th Grade, 7th Grade, and 8th Grade.

  13. 7.1.4: The Pythagorean Theorem

    Summary. The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the triangle's legs is the same as the square of the length of the triangle's hypotenuse. This theorem is represented by the formula a 2 + b 2 = c 2.

  14. Unit 8

    Unit 8 - The Pythagorean Theorem. Lesson 1. The Pythagorean Theorem. LESSON/HOMEWORK. LECCIÓN/TAREA. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY.

  15. Homework

    Below is an outline for a proof of the Pythagorean theorem's converse. Complete the proof by filling in the reasons. Suppose you have some triangle ABC, where the lengths of the sides satisfy the relationship a 2 + b 2 = c 2. a. Construct a right triangle with legs a and b (so there is a right angle between the sides with lengths a and b).

  16. 3.5: Triangles, Rectangles, and the Pythagorean Theorem

    Figure 3.5.1 3.5. 1: Triangle ABC has vertices A A, B B, and C C. The lengths of the sides are a a, b b, and c c. The three angles of a triangle are related in a special way. The sum of their measures is 180∘ 180 ∘. Note that we read m∠A m ∠ A as "the measure of angle A.". So in ABC A B C in Figure 3.5.1 3.5.

  17. 20 Pythagorean Theorem Worksheet with Answers (Word & PDF)

    Today, it has many applications in different areas of study, from simple elementary and high school geometry to complex engineering and architecture calculations. Below, we take a closer look at the theorem and how you can master it through a worksheet. What Is a Pythagorean Theorem Worksheet?

  18. 9.1: The Pythagorean Theorem

    The Pythagorean Theorem says that. a2 +b2 = c2. a 2 + b 2 = c 2. In this example, the legs are known. Substitute 4 for a and 3 for b (3 for a and 4 for b works equally well) into the Pythagorean equation. 42 +32 = c2 4 2 + 3 2 = c 2. 3. Solve the Equation. 42 +32 = c2 16 + 9 = c2 25 = c2 5 = c The Pythagorean equation.

  19. PDF Looking for Pythagoras: Homework Examples from ACE

    a. Applying the Pythagorean Theorem 2.52 + 62 = a2. So, 42.25 = a2. So, a = 6.5 cm. b. To find the volume you need to know the area of the base of the prism and the height of the prism. The area of the base is 0.5 (2.5 x 6) = 7.5 square units. You don't need to know a to find this base area. To find the surface area you need to know the areas

  20. 4.31: Converse of the Pythagorean Theorem

    The Converse of the Pythagorean Theorem. The Pythagorean Theorem states that for a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem can be modeled by the equation \(c^2=a^2+b^2\) where '\(c\)' represents the length of the hypotenuse, 'a' represents the length of one leg and '\(b\)' represents ...

  21. PDF learning focus

    Learn how to apply the Pythagorean Theorem to solve real-world and mathematical problems with this 8th grade CCSS-aligned unit. This preview pdf includes an overview of the unit, a pacing guide, and sample pages from the student and teacher materials. Download it for free and see how Maneuvering the Middle can help you teach engaging and rigorous math lessons.

  22. Math Medic

    Day 5: Right Triangles & Pythagorean Theorem; Day 6: Coordinate Connection: Distance ; Day 7: Review 4.1-4.6; ... Answer Key. pdf. Media Locked ... On homework and assessment questions, we like to label the side lengths as d, o, and g or some other three letter word and have students write an equation relating the three sides. ...

  23. 3.4: Triangles, Rectangles, and the Pythagorean Theorem

    P = a + b + c. Area: A = 12bh, b=base,h=height. A right triangle has one 90° angle. The Pythagorean Theorem In any right triangle, a2 +b2 = c2 where c is the length of the hypotenuse and a and b are the lengths of the legs. Properties of Rectangles. Rectangles have four sides and four right (90°) angles.