1/12/2024 0 Comments Converse geometry example![]() The converse of the Pythagoras theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. How Do You Prove the Converse of Pythagoras Theorem? The converse of Pythagoras theorem formula is c 2 = a 2 + b 2, where a, b, and c are the sides of the triangle. What is the Formula for Converse of Pythagoras Theorem? The coverse of the Pythagoras theorem states that, in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. In other words, we can say, in a right triangle, (Opposite) 2 + (Adjacent) 2 = (Hypotenuse) 2.įAQs on Converse of Pythagoras Theorem What is the Converse of Pythagoras Theorem? Here, AB is the base, AC is the altitude or the height, and BC is the hypotenuse. In the given triangle ABC, we have BC 2 = AB 2 + AC 2. The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. If the sum of the squares of two sides of a triangle is greater than the square of the hypotenuse, the triangle is an acute triangle. If the sum of the squares of two sides of a triangle is less than the square of the hypotenuse, the triangle is an obtuse triangle.ģ. If the sum of the squares of two sides of a triangle is considered equivalent to the square of the hypotenuse, the triangle is a right triangle.Ģ. Once the triangle is identified, constructing that triangle becomes simple. The main application of the converse of the Pythagorean theorem is that the measurements help in determining the type of triangle - right, acute, or obtuse. The converse is the complete reverse of the Pythagoras theorem. The converse of Pythagoras theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. The logical result of all this work with converse, inverse, contrapositive, and counterexample logical statements is, we learn that Jennifer is a living, breathing woman who eats.What is the Converse of Pythagoras Theorem? Surely you can see - leaving out zombies and vampires and other imaginary creatures - that we cannot produce a counterexample for any of our logical statements our argument is valid. If we can find such an example, even a single example, in which the premises are valid but the conclusions are false, we would have a counterexample showing the original argument is invalid. We would need to find a single example of one of these conditions, any one of which would be a counterexample:Ī woman who eats food but who is not alive, orĪ woman who does not eat food but who is alive Inverse: If Jennifer is not alive, then Jennifer does not eat food.Ĭontrapositive: If Jennifer does not eat food, then Jennifer is not alive. ![]() Original statement: If Jennifer is alive, then Jennifer eats food.Ĭonverse: If Jennifer eats food, then Jennifer is alive. We need only find one instance, called a counterexample, where the conditions set out in our arguments are not valid: If you can find a substitute that tests the logical validity of the statement (but not its factual accuracy), you know the claim is not always true and is therefore not logically valid. If the logical contrapositive statement is false, then the conditional statement itself is also false. If the conditional statement is true, then the logical contrapositive statement is true. If Jennifer does not eat food, then Jennifer is not alive. They can produce logical equivalence for the original statement, but they do not necessarily produce logical equivalence. Statements 2 and 4 are logical statements statement 1 is an opinion, and statement 3 is a fragment with no logical meaning.įour testable types of logical statements are converse, inverse, contrapositive, and counterexample statements. Mint chocolate chip ice cream is delicious.įricasé de Pollo is a type of Cuban food. Which of these phrases or utterances is a logical statement? Remember, it need not be true, just testable. The second statement is logical but not factual. ![]() We know the second statement can be tested for its truthfulness. The first statement is an opinion and is neither logical nor factual it cannot be tested to be true. ![]() One is an opinion, which cannot be tested for truthfulness: For example, one of the two statements below is logical in that they can be tested for its truthfulness. Logical statements must be tested to be valid. Some of those structures of formal logic are converse, inverse, contrapositive, and counterexample statements. Logic is a learned mathematical skill, a method of ferreting out truth using specific steps and formal structures. Most humans do not begin to learn logic until they are around 10 years old.
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