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Pythagorean Relationship 2 (Finding the length of the Hypotenuse)Measurement Pythagorean Relationship 2 (Finding the length of the Hypotenuse)
To review… In a right angle triangle, the side of the triangle opposite the right angle is called the hypotenuse. hypotenuse legs
Pythagorean RelationshipArea = c2 b c Area = b2 c b a a2 + b2 = c2 a Area = a2
Applying the Pythagorean RelationshipWe know that: a b2 = c2 a c b
Applying the Pythagorean RelationshipUsing this… If we know the lengths of ANY two sides of a right angle triangle, we can use the Pythagorean Relationship to find the length of the unknown side. a c b
Applying the Pythagorean RelationshipSituation One: We know the lengths of the two legs (a and b) of a right triangle. How can we find the length of the hypotenuse (c)? a c b
Applying the Pythagorean RelationshipSince we know that: a2 + b2 = c2 Then: c2 = a2 + b2 a c b
Applying the Pythagorean RelationshipSince: c2 = a2 + b2 Then: c = (a2 + b2) a c b
Applying the Pythagorean RelationshipExample: a = 7m; b = 5m c = (a2 + b2) c = ( ) c = ( ) c = c = m a = 7m c = ? b = 5m
Problem a = 3cm Find the length of the hypotenuse, “c”. b = 6cm c = ?
Pythagorean Theorem Properties of Special Right Triangles
Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)
Pythagoras Bingo. Pick 8 from the list C no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.
The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.
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EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.
EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.
The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.
EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.
Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’
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Pythagorean Theorem Mr. Parks Algebra Support. Objective The student will be able to: Find the missing side of a right Triangle using the Pythagorean.
What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side.
MA.912.G.5.1 : Apply the Pythagorean Theorem and its Converse. A.5 ft B.10 ft C. 15 ft D. 18 ft What is the value of x? x 25 ft 20 ft.
Ch 9.1 The Pythagorean Theorem Definition of the Day Right Triangle Legs of a Triangle Hypotenuse of a Triangle The Pythagorean Theorem.
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Section 3-5 p. 137 Goal – to solve problems using the Pythagorean Theorem.
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