Converse Of The Pythagorean Theorem Answer Key The Converse of the Pythagorean Theorem Words If the square of the length of the B longest side of a triangle is equal c a to the sum of the squares of the lengths of the other two sides then C b A the triangle is a right triangle Symbols If c2 5 a2 1 b2 then TABC is a right triangle Student Help
Example 1 The Converse of the Pythagorean Theorem What can the converse of the Pythagorean theorem be used for Demonstrating that a triangle is equilateral Demonstrating that a triangle has a right angle Finding the angles in a triangle Finding lengths in an equilateral triangle Demonstrating that a triangle is an isosceles triangle Answer Yes No No 14 9 in 12 in 15 in Yes Yes State if each triangle is acute obtuse or right 15 Obtuse Acute 18 4 8 km 28 6 km 29 km Obtuse Right Create your own worksheets like this one with Infinite Geometry Free trial available at KutaSoftware
Converse Of The Pythagorean Theorem Answer Key
Converse Of The Pythagorean Theorem Answer Key
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Converse Of Pythagorean Pythagoras Theorem Definition Formula
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The converse of the Pythagorean Theorem is 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 That is in ABC A B C if c2 a2 b2 c 2 a 2 b 2 then C C is a right triangle PQR P Q R being the right angle 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
The converse of Pythagoras theorem is the reverse of the Pythagoras theorem and it helps in determining if a triangle is acute right or obtuse if the sum of the squares of two sides of a triangle is compared to the square of its third side The Pythagorean theorem is the most used in trigonometry The 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 c2 a2 b2 then the triangle is a right triangle with c its hypotenuse
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Think about what you have learned about the Pythagorean Theorem and answer true or false for the following questions 1 The Pythagorean Theorem will work for an acute triangle with all 60 angles 2 The Pythagorean Theorem will work for a right triangle 3 The Pythagorean Theorem will only work if the triangle is a right triangle 4 Solution We choose the two shorter sides to be a and b and the longest side to be c So a 3 b 5 and c 7 a 2 b 2 3 2 5 2 9 25 34 c 2 7 2 49 49 34 c 2 a 2 b 2 and so the triangle is an obtuse triangle Example Determine whether a triangle with sides 12 cm 14 cm and 18 cm is an acute right or obtuse triangle
1 Plan What You ll Learn To use the Pythagorean Theorem To use the Converse of the Pythagorean Theorem Check Skills You ll Need Square the lengths of the sides of each triangle What do you notice 753 GO for Help Skills Handbook p A 1 1 32 42 52 m 3 5 m 2 52 122 132 B C 4 m 2 A 13 in 5 in C B 12 in Unit 1 Right Triangles and the Pythagorean Theorem
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