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.

Find the value of x.

• 7

• 8

• 9

• 10

Answer explanation

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

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)

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

$c\approx6.3$

Find the value of x.

Mathematical Equivalence

ON

A 10-foot ladder is leaning against the wall. The bottom of the ladder is 4 feet from the base of the wall. Which of the following is closest to the distance from the top of the ladder to the base of the wall?

• 9ft

• 11ft

• 6ft

• 14ft

_{^{Find the missing side}}

• 48

• 108

• 83.6

• 72

Find the missing length indicated. Leave your answer in simplest radical form.

• 64

• 12

• 9

• 100

Solve for the length indicated.

• 1

• 2

• 3

• 4

Find the value of x. Round your answer to the nearest tenth.

Mathematical Equivalence

ON