PYTHAGOREAN THEOREM AND ITS CONVERSE ANSWERS
Pythagorean Theorem (solutions, examples, answers
This video shows how to use the Pythagorean Theorem and its Converse to determine if a triangle is acute, right, or obtuse. According to the triangle inequality theorem , the sum of the two shorter sides of a triangle must be greater that the longest side.[PDF]
8-The Pythagorean Theorem and Its Converse
The Pythagorean Theorem and Its Converse Date_____ Period____ Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. 1) x 12 in 13 in 5 in 2) 3 mi 4 mi x 5 mi 3) 11.9 km x 14.7 km 8.6 km 4) 6.3 mi x 15.4 mi 14.1 mi Find the missing side of each triangle. Leave your answers in simplest radical form. 5) x[PDF]
8-1 The Pythagorean Theorem and Its Converse
Theorems 8-1 and 8-2 Pythagorean Theorem and Its Converse A c b a C B c 24 10 203 Lesson 8-1 Converse of the Pythagorean Theorem If the sum of the squares Answers may vary. Sample: The numbers are the same as the lengths of the sides of the triangle in Exercises 9–11. 10 24
The Pythagorean Theorem and Its Converse? | Yahoo Answers
Jul 05, 2006The Pythagorean Theorem and Its Converse? Once you believe the Pythagorean theorem, its converse follows very nicely in Euclid's Elements, Book I, Proposition 48. You should check it out, those books are famous for a reason! Help with Pythagorean Theorem and its converse please? More questions.Status: ResolvedAnswers: 14A(squared) + B(squared) = C (squared)
C(squared) - B(squared) = A (squared)
C(squared)- A(squared) = B squared.Best answer · 0This is NOT sa converse -- this is an inverse. 12 units can be divided into 3, 4, and 5. so holding the rope at the appropriate knots against two sides that meet at a point will confirm that the rope fits snugly, with hypotenuse of 5. However if you hold the wrong knots you cannot confirm the result as a right angle.
It is NOT a good way, for several reasons: knots are not fine enough to serve as "point" vertices of a triangle, so the accuracy will be low (you could probably not tell the difference between 85 degrees and 90 degrees. Furthermore any triangle whose integral sides total to 12 could fit the rope. The nearest is the triangle 4 x 4 x 4 which identifies a 60 degree angle which is significantly different from 90 degrees, but that is "accidental": if you tried it with 30 knots, this would form a 5x12x13 Pythagorean triangle, but 5 x 11 x 14 forms a NON-Pythagorean triangle with one angle that may "look" like 90 degees to the untrained eye.0Given that 12 equally-spaced knots are tied in 1 rope, the rope has been divided into 12 equal segments. You can form a triangle with this rope by forming an angle at each interval of 3 knots, 4 knots, and 5 knots. You now have a right triangle, proven by the Pythagorean Theorem.
Pythagorean Theorem: Given a triangle: a and b are the legs; c is the hypotenuse.
a squared + b squared = c squared
In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.
Therefore: 3 squared + 4 squared = 5 squared
9 + 16 = 25
25 = 25
Proof of the Converse: The rope forms a right angle because the triangle it forms can be proven to be a right triangle by the Pythagorean Theorem.0Pythagoras's Theorem states that the square of the hypotenuse in a right angled triangle is equal to the sum of the squares of the other two sides. The classic right angled triangle has sides of 3, 4 and 5 so:-
3 x 3 = 9
4 x 4 = 16
Add 9 and 16 = 25
5 x 5 = 25
Now then 3 = 4 = 5 = 12 so if you make a right angle anywhere on the knots on the rope, according to your calculations (by the way you'd need 13 knots as you need 12 spaces.) you should be able to prove it. However if one side is 11 that leaves you with 1 and nothing for the hypotenuse so the rope theory doesn't work. It will for a 3, 4, 5 triangle though.0WTF, sound to me like people have the wrong notion of what the converse is a statement.
Dude, you answer can be found in symbolic logic (which is used to done proofs in math, which is why it helps if you look at the proof of whatever it is you are trying to understand.)
Here is some basic logic.
If I have a statement a=>b (a implies b, if a then b, a arrow b)
converse is b=>a
inverse is ~a=>~b
contrapositive is ~b=>~a
~ symbol means "not" like the negation in English
Notice that the inverse is just converse contrapositive or the converse is the inverse contrapositive. And also out of all of these the contrapositive is the most important because the contrapositive has the property of being exactly equal to the original statement. We use this fact when we are doing proofs by contradiction which makes it really easy.
Okay, here is your answer. Out of all four of these, if the statement is true(or false), then the ONLY the contrapositive is guaranteed to be true(or false). You have no idea about the other two. You cannot say if the inverse is also true (or false) or if the converse is true (or false).
Now, it turns out that you can only say something about the converse and the inverse if the original statement a=>b is actually a<=>b (a double-arrow b, a if and only if b, a equivalent to b).
If you know that the statement a<=>b is true, then the inverse, converse, and the contrapositive are all true.
That's why the converse to the pythogorean theorem works. Because the statements
a=the triangle is a right triangle
b=one leg^2 + other leg^2 = hypotenuse ^2
were proven to be equivalent.
So I can assume a and prove b or I can assume b and prove a. Which means I can assume a and b will always be true or I can assume b and a will always be true.0The reason the converse works is because of the properties of congruent and similar triangles.
Remember in geometry class when you defined congruent triangles as those with three pairs of corresponding sides congruent and three pairs of corresponding angles congruent? Then you learned this happy short-cut called "SSS," or the side-side-side theorem?
Imagine a 3:4:5 triangle. You know this triangle to be a right triangle. Because of SSS, any other triangle that measures 3:4:5 (of the same unit) has to be congruent, and therefore must have a right angle opposite from the hypotenuse.
With similar triangles, the pairs of corresponding angles must all be congruent. The lengths of the sides of one triangle may differ, but they'll be in proportion to the corresponding sides of the other triangle.
Take your looped rope. Measure 12 equally-spaced knots in it. Pull out the sides in proportion to 3:4:5 knots. This triangle, no matter how far apart the knots are spread, is in proportion to any 3:4:5 triangle. They make similar triangles, which means the angles on each must be congruent.
Therefore, regardless of the space between each of the knots on your rope, as long as the sides of the triangle are in a 3:4:5 ratio, it will have a right angle opposite the longest side.03, 4, 5 is a pythagorean triple (numbers that satisfy the pythagorean theorem)
3+4+5=12 which means if you connect the rope from end to end, you'll form a 3-4-5 right triangle.0a^2+ b^2=c^2
3^2+ 4^2= 5^2
9+16=250Well, all bulding sites use the 3, 4, 5. They get a triangle with one side 3 feet, and one 4 feet and the final one five and that's a perfect right angle. We can note that 3, 4, and 5 make 12; so that's why it works.012 = 3 + 4 + 5.. 3^2 + 4^2 = 5^2
so one right triangle measures 3,4,5.. if you take your rope, put 3 knots on one wall to the corner, 4 knots along the other wall.. if it is 5 knots back out in open air. then the wall's corner is square.0
Pythagorean Theorem and Its Converse - CliffsNotes
wwwfsnotes›Study Guides›GeometryThe converse (reverse) of the Pythagorean Theorem is also true. Theorem 66: If a triangle has sides of lengths a, b, and c where c is the longest length and c 2 = a 2 + b 2, then the triangle is a right triangle with c its hypotenuse.
Applying the Pythagorean Theorem - CPALMS
This lesson applies the Pythagorean Theorem and teaches the foundational skills required to proceed to lesson 2, Origami Boats - Pythagorean Theorem in the real world Resource ID 49055. This lesson should not be taught until the students have a knowledge of standard MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse.
Pythagorean Theorem Proofs and its Converse Worksheets
wwwworksheetsland›Grade Levels›Grade 8Pythagorean Theorem Proofs and its Converse. Aligned To Common Core Standard: Pythagorean Theorem Worksheet Five Pack Version 2 - Half word problems and half in your face triangles. Answer Keys View Answer Keys- All the answer keys in one file.[PDF]
7.1 Apply the Pythagorean Theorem - Denton ISD
7.1 Apply the Pythagorean Theorem Obj.: Find side lengths in right triangles. Key Vocabulary 7.2 Use the Converse of the Pythagorean Theorem Obj.: Use its converse to determine if a triangle is a right triangle. Key Vocabulary Write each answer as a [PDF]
Lesson 8-2 Pythagorean Theorem and its Converse with
Lesson 82 Pythagorean Theorem and its Converse with answersbook 2 February 09, 2015 Questions/Main IdeasPythagorean Triple three whole numbers that satisfy the equation where c is the greatest number Example 2 Use a Pythagorean triple to find x. Explain your reasoning.
Can you give me a practical application of Pythagoras's
Jul 11, 2009The most widely quoted "practical" application of the Pythagorean theorem is actually an application of its converse. The theorem of Pythagoras says that if a triangle has sides of length a, b and c and the angle between the sides of length a and b is a right angle, then a^2 + b^2 = c^2.Status: ResolvedAnswers: 8People also askWhat is the Pythagorean theorem formula?What is the Pythagorean theorem formula?The Pythagorastheorem says that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and the base. The Pythagorean Theorem formula is given as: Where His the length of the hypotenuse,P is the length of the perpendicular,and B is the length of the base.The Pythagorean Theorem Formula and its ApplicationsSee all results for this questionHow to solve the Pythagorean theorem?How to solve the Pythagorean theorem?How to Solve Pythagoras Theorem Questions - Finding the Diagonal of a RectangleEnsure the polygon is a rectangle.Make sure you have the length and width of the rectangle.Locate or draw the diagonal of the rectangle.Set up the formula for Pythagoras’s Theorem.Plug the values of the rectangle’s length and width into the formula... (more items)How to Solve Pythagoras Theorem Questions: 2 StepsSee all results for this questionHow do you find the third side of a triangle?How do you find the third side of a triangle?To findthe thirdangle of a triangle,start by adding the other 2 angles together. Then,subtract that number from 180 to findthe thirdangle. If the 2 known angles have variables,start by adding all of the measurements,including the variable used for the unknown angle.3 Ways to Find the Third Angle of a Triangle - wikiHowSee all results for this questionWhat is the converse of corresponding angles theorem?What is the converse of corresponding angles theorem?Accoridingto corresponding angles theorem,when there are two lines that are parallel to each other,and there is one line that passes through both line (we call this line 'transversal'),then two corresponding angles are equal. The corresponding angles CONVERSE is exactly the opposite.Reference: wwwg/tutors/what-is-Corresponding-Angles-Converse/See all results for this question
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