Holt Course 2 NY-10 Using the Pythagorean Theorem NY-10 Using the Pythagorean Theorem Holt Course 2...
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Holt Course 2 NY-10 Using the Pythagorean Theorem NY-10 Using the Pythagorean Theorem Holt Course 2 Lesson Presentation Lesson Presentation
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Transcript of Holt Course 2 NY-10 Using the Pythagorean Theorem NY-10 Using the Pythagorean Theorem Holt Course 2...
Holt Course 2
NY-10 Using the Pythagorean TheoremNY-10 Using the Pythagorean Theorem
Holt Course 2
Lesson PresentationLesson Presentation
Holt Course 2
NY-10 Using the Pythagorean Theorem
Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator.
Objective
Holt Course 2
NY-10 Using the Pythagorean Theorem
The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
The Pythagorean Theorem also works in “reverse.” If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the remaining side, then the triangle is a right triangle.
a2 + b2 = c2 a c
b
Holt Course 2
NY-10 Using the Pythagorean Theorem
Example 1A: Determining if a Triangle is a Right Triangle
The side lengths of a triangle are shown. Determine whether the triangle is a right triangle.
The triangle is not a right triangle.
13 ft, 17 ft, 21 ft
Compare a2 + b2 = c2.
Substitute the longest side length for c.
Use a calculator.
a2 + b2 = c2
132 + 172 = 212
458 441
?
?
Holt Course 2
NY-10 Using the Pythagorean Theorem
Example 1B: Determining if a Triangle is a Right Triangle
The side lengths of a triangle are shown. Determine whether the triangle is a right triangle.
The triangle is a right triangle.
20 ft, 21 ft, 29 ft
Compare a2 + b2 = c2.
Substitute the longest side length for c.
Use a calculator.
a2 + b2 = c2
202 + 212 = 292
841 = 841
?
?
Holt Course 2
NY-10 Using the Pythagorean Theorem
Check It Out! Example 1A
The side lengths of a triangle are shown. Determine whether the triangle is a right triangle.
9 cm, 40 cm, 41 cm
The triangle is a right triangle.
Compare a2 + b2 = c2.
Substitute the longest side length for c.
Use a calculator.
a2 + b2 = c2
92 + 402 = 412
1681 = 1681
?
?
Holt Course 2
NY-10 Using the Pythagorean Theorem
Check It Out! Example 1B
The side lengths of a triangle are shown. Determine whether the triangle is a right triangle.
5 ft, 18 ft, 19 ft
The triangle is not a right triangle.
Compare a2 + b2 = c2.
Substitute the longest side length for c.
Use a calculator.
a2 + b2 = c2
52 + 182 = 192
349 361
?
?
