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The Pythagorean Theorem proofs exercise appears under the 8th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise develops understanding of several proofs of the Pythagorean Theorem.

Types of Problems

There are three types of problems in this exercise:

  1. Slide the steps and reasons into order: This problem provides the steps and justifications for a proof of the Pythagorean Theorem. The user is asked to put the statements and reasons in the correct order.
    Ptp1

    Slide the steps and reasons into order

  2. Select the correct answers from drop-downs: This problem provides a proof of the Pythagorean Theorem with a few missing pieces. Users are asked to complete the proof using options from drop-down menus.
    Ptp2

    Select the correct answers from drop-downs

  3. Select the incorrect step: This problem provides a proposed proof of the Pythagorean Theorem that is not valid. The user is asked to find the first incorrect step in the supposed proof.
    Ptp3

    Select the incorrect step

Strategies

The Pythagorean Theorem is one of the most famous theorem in all of mathematics. Researching and knowing a few of the standard proofs of this theorem could assist on this exercise.

  1. One of the proofs used is the Bhaskra proof.
  2. One of the proofs used is the Garfield proof.
  3. All of the proofs use geometric area formulas. Triangles and quadrilaterals may both appear.

Real-life applications

  1. The Pythagorean Theorem was famously used in ancient Egypt for creating monuments and ensuring measuring objects.
  2. Mathematical logic and reasoning can be used to strengthen writing and reasoning skills in general.

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