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8.1 handout pythagorean theorem and its converse.notebook 1 March 14, 2016 Geometry Ch. 8 Handout 8.1 The Pythagorean Theorem and its Converse

Transcript of 8.1 handout pythagorean theorem and its converse.notebook Pythagorean... · 8.1 handout pythagorean...

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GeometryCh. 8   Handout 8.1  

                  The Pythagorean Theorem                         and its Converse

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Pythagorean Theorem1.2.

Works only on right triangles.

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

  a(leg)

  b(leg)

 c(hypotenuse)

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A Pythagorean Triple is a set of nonzero whole numbers a, b, and c that satisfy the equation                             Here are some common Pythagorean triples:

3, 4, 5 5, 12, 138, 15, 17 7, 24, 25

If you multiply each number in a Pythagorean triple by the same whole number, the three numbers that results also form a Pythagorean triple.

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1.  Find the length of the hypotenuse of 

A

B

C

12

5

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2.  A right triangle has a hypotenuse of length 25 and a leg of length 10.  Find the length of the otherleg.  

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3.  Find the value of b.  Leave you answer in simplest radical form.a.

12 8

b

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3.  Find the value of b.  Leave you answer in simplest radical form.

b.8

14

x

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3.  Find the value of b.  Leave you answer in simplest radical form.

c.9

12

x

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4.  The hypotenuse of a right triangle has length 12.  One leg has length 6.  Find the length of the other leg.  Leave your answer in simplest radical form.

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5.  A baseball diamond is a square with 90­ft sides.  Home plate and second base are at opposite vertices of the square.  About how far is home plate from second base?

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Theorem 8­2:  Converse of Pythagorean TheoremIf the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

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Theorem 8­3If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse.

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Theorem 8­4If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute.

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is a right triangleis an obtuse triangleis an acute triangle

a

b

c

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Classify each triangle as Acute, Obtuse, or Right Triangle.

4 m

6 m7 m

26 m 24 m

10 m

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Classify each triangle as Acute, Obtuse, or Right Triangle.

10, 15, and 201) 16, 48, and 502)

3) 7, 8, and 9

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6.  The town of Elena is 24 mi north and 8 mi west of Holberg.  A train runs on a straight track between the two towns.  How many miles does it cover?  Round your answer to the nearest whole number.

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What is the distance from A to B? (to the nearest mile)

210 m

South Dakota

What is the distance from A to B? (to the nearest mile)

North Dakota

A

B340 m

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12 ft

43 ft

How high off the ground is Ollie the owl?

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Assignment:

Day 1:  pgs 420­421  1­15 odds, 17, 27, 29

Day 2:  pgs 420­421  2­16 evens, 18­26 all, 28, 59­64