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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

6. The Converse of the Pythagorean Theorem

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Exercise 12 Page 413

Use the Converse of the Pythagorean Theorem.

Yes.

Practice makes perfect

We are given the lengths of the three sides of a triangle, and want to determine whether the sides form a right triangle. We will need to use the Converse of the Pythagorean Theorem.

Converse of the Pythagorean Theorem
If the sides of a triangle have lengths a, b, and c, and c^2=a^2+b^2, then the triangle is a right triangle.

This tells us that we can use the Pythagorean Theorem in reverse to test if a triangle is right. In general, the hypotenuse c has the greatest value. Let's substitute a= 910miles, b=1 15miles, and c=1 12miles into a^2+b^2=c^2, and see if they produce a true statement.

a^2+b^2=c^2

SubstituteValues

Substitute values

( 9/10)^2+( 1 15)^2? =( 1 12)^2

▼

Simplify

a bc=a* c+b/c

(9/10)^2+(1 * 5+1/5)^2? =(1 * 2+1/2)^2

Identity Property of Multiplication

(9/10)^2+(5+1/5)^2? =(2+1/2)^2

Add terms

(9/10)^2+(6/5)^2? =(3/2)^2

(a/b)^m=a^m/b^m

9^2/10^2+6^2/5^2? =3^2/2^2

Calculate power

81/100+36/25? =9/4

a/b=a * 4/b * 4

81/100+36 * 4/25 * 4? =9/4

Multiply

81/100+144/100? =9/4

Add fractions

81+144/100? =9/4

Add terms

225/100? =9/4

a/b=.a /25./.b /25.

225/25/100/25? =9/4

Calculate quotient

9/4 = 9/4 ✓

The values produce a true statement, so the described triangle is a right triangle.

Subchapter links

Try It p.410-411

Self-Assessment for Concepts & Skills p.411-412

Review & Refresh p.413

Concepts, Skills, & Problem Solving p.413-414