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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

2. The Pythagorean Theorem and Its Converse

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Exercise 47 Page 554

Use the Pythagorean Theorem.

1/2

Practice makes perfect

To find the missing side of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=sqrt(2), b=x, and c=x+1.

Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

( sqrt(2))^2+ x^2=( x+1)^2

▼

Solve for x

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

(sqrt(2))^2+x^2=x^2+2* 1* x + 1^2

Calculate power

2+x^2=x^2+2* 1* x + 1

Multiply

2+x^2=x^2+2x+ 1

LHS-x^2=RHS-x^2

2=2x+ 1

LHS-2=RHS-2

0=2x-1

LHS-2x=RHS-2x

- 2x= - 1

.LHS /(- 2).=.RHS /(- 2).

x = 1/2

Subchapter links

Check Your Understanding p.551-552

Practice and Problem Solving p.552-554

H.O.T. Problems p.554

Standardized Test Practice p.555

Spiral Review p.555

Skills Review p.555