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Published byBrittany Burns Modified over 4 years ago

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**8-1, 1-8 Pythagorean Theorem, Distance Formula, Midpoint Formula**

Objectives Apply the Pythagorean Theorem Determine whether a triangle is acute, right, or obtuse Apply the distance formula Apply the midpoint formula

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**Right Triangles A right triangle is a triangle with a right angle**

ypotenuse hypotenuse leg egs leg A right triangle is a triangle with a right angle

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**Pythagorean Theorem (leg1)2 + (leg2)2 = hypotenuse2**

True only for right triangles

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**Pythagorean Theorem Example**

2 Leg1 = ? 6 Pythagorean Theorem 22 + X2 = 62 X2 = 62 – 22 X2 = 36 – 4 = 32 X = 32 X ≅ 5.7

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**Determining Acute, Right, or Obtuse for Triangles**

Let a, b, c be the lengths of the sides of a triangle, where c is the longest Acute: c2 < a2 + b2 Right: c2 = a2 + b2 Obtuse: c2 > a2 + b2 A triangle’s sides measure 3, 4, 6 62 ? 36 > = 25 Obtuse

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**Distance on number line**

-3 -1 -2 1 -8 2 -7 -5 -6 -4 Find AB (distance between A and B) AB = | -8 – (-5) | = | -3 | = 3

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**Distance in the coordinate plane**

y x C(2, 3) 1) On graph paper, plot A(-3, 1) and C(2, 3). A(-3, 1) 2) Draw a horizontal segment from A and a vertical segment from C. B(2, 1) 3) Label the intersection B and find the coordinates of B. QUESTIONS: What is the horizontal distance between A and B? (2 – -3) = 5 What is the vertical distance between B and C? (3 – 1) = 2 What kind of triangle is ΔABC? right triangle If AB and BC are known, what theorem can be used to find AC? Pythagorean Theorem What is the measure of AC? 29 ≈ 5.4

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**Distance formula in the coordinate plane**

y x A(x1, y1) B(x2, y2) d then d =

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**Midpoint on a number line**

4 6 6 M = ? The location of the midpoint is the average of the endpoints M = M = 5

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**Midpoint on the coordinate plane**

Graph A(1, 1) and B(7, 9) y x 10 -1 2 4 6 8 -2 3 7 1 5 9 Draw AB B(7, 9) Find the midpoint of AB. C C(4, 5) A(1, 1) C = (4, 5)

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