9E: Applying Pythagorean Theorem

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Answer explanation

The pythagorean theorem only works for right triangles.

Tags

CCSS.8.G.B.8

Name the longest side of a right triangle.

• leg a

• leg b

• leg

• hypotenuse

Answer explanation

The longest side of a right triangle is the hypotenuse, the side opposite of the right angle.

The side lengths of a right triangle are 24, 45 and 51. Which side is the hypotenuse?

• 51

• 24

• 45

• Can't determine

Answer explanation

The hypotenuse is always the longest side. For a triangle with lengths 24, 45, and 51, 51 is the longest side.

Tags

CCSS.HSG.CO.C.10

The Pythagorean Theorem is

a² + b³ = c⁴

• false

• true

Answer explanation

The pythagorean theorem for right triangles is: $a^2+b^2=c^2$

Tags

CCSS.8.G.B.8

What is the final step in solving this work for c?

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

• Divide both sides by 2

• Take the square root of both sides

Answer explanation

$25=c^2$
The next step is to use an inverse operation to "unravel" the exponent above c.

$\sqrt{25}=\sqrt{c^2}$
$5=c$
(Triangles can only have positive side lengths)

Tags

CCSS.8.G.B.8

Find the value of x.

• 7

• 8

• 9

• 10

Answer explanation

$a^2+b^2=c^2$
$6^2+8^2=x^2$
$36+64=x^2$
$100=x^2$
$\sqrt{100}=\sqrt{x^2}$
$10=x$

Tags

CCSS.8.G.B.7

^{Find the missing side (hint: use what you know about estimating irrational numbers to answer)}

• 9

• 41

• 6.4

• 6.2

Answer explanation

$a^2+b^2=c^2$
$5^2+4^2=c^2$
$25+16=c^2$
$41=c^2$
$\sqrt{41}=\sqrt{c^2}$

$\sqrt{36}<\sqrt{41}<\sqrt{49}$
$6<\sqrt{41}<7$

$c\approx6.4$
(is between 6 and 7, slightly closer to 6)

Tags

CCSS.8.G.B.7

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Answer explanation

$a^2+b^2=c^2$
$y^2+12^2=13^2$
$y^2+144=169$
$y^2+144-144=169-144$
$y^2=25$
$\sqrt{y^2}=\sqrt{25}$

$y=5$
(triangles can only have positive side lengths)

Tags

CCSS.8.G.B.7

Find the distance between these two points. Use what you know about pythagorean theorem and estimating irrationals.

• 6.3

• 6.5

• 6.7

• 16

Answer explanation

Distance between y-values, vertical: 3-1 = 2
Distance between x-values, horizontal: 4-(-1) = 6

$a^2+b^2=c^2$

$2^2+6^2=c^2$
$4+36=c^2$
$40=c^2$
$\sqrt{40}=\sqrt{c^2}$

$\sqrt{36}<\sqrt{40}<\sqrt{49}$
$6<\sqrt{40}<7$
*between 6 and 7, but closer to 6

$c\approx6.3$

Tags

CCSS.HSG.GPE.B.7