9F: Pythagorean Theorem Converse

What is the formula for Pythagorean theorem?

• a²⁺b²=c²

• a+b=c

• a-b=c

• c-a=c

Tags

CCSS.HSG.SRT.B.4

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Tags

CCSS.8.G.B.8

What is the longest side of a right triangle called?

• Leg A
• Leg B
• Hypotenuse
• Pythagoras' Big Buddy

Tags

CCSS.HSG.SRT.C.8

Which variable in the pythagorean theorem represents the hypotenuse of a right triangle?  $a^2+b^2=c^2$  

•  $a$  

•  $b$  

•  $c$  

•  $c^2$  

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CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Which statement is the MOST accurate about the converse of the Pythagorean Theorem?

• The converse is used to determine an unknown side length.

• The converse is only useful with right triangles

• The converse is used to determine if a triangle is or is not a right triangle

• The converse always works out that a²+b²=c²

Answer explanation

The Converse of the Pythagorean Theorem states:

IF
$a^2+b^2=c^2$
(where c is the longest side length)

THEN

The triangle is a right triangle.

Tags

CCSS.HSG.SRT.B.4

Given the 3 lengths of a triangle are 6 in, 8 in and 10 in. Will this make a right triangle?

• yes

• no

Answer explanation

$6^2+8^2=10^2\ ?$
$36+64=100\ ?$
$100\ =\ 100$
This is true, so the side lengths do form a right triangle.

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CCSS.HSG.SRT.B.4

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Can side lengths 3, 4, and 5 form a right triangle?

• yes

• no

Answer explanation

$3^2+4^2=5^2\ ?$
$9+16=25\ ?$
$25\ =\ 25$
This is true, so the side lengths do form a right triangle.

Tags

CCSS.HSG.SRT.C.8

Define a Pythagorean Triple

• When all three sides of a right triangle are whole numbers

• Three sides are equal lengths

• Two sides are equal in length

• When you add every number together to find the missing length

Answer explanation

A Pythagorean Triple:
When all three sides of a right triangle are whole numbers

Example: 3, 4, 5

$3^2+4^2=5^2$
$9+16=25$
$25\ =\ 25$

Tags

CCSS.HSG.SRT.C.8

Does the set of numbers represent a Pythagorean Triple? (Use the Pythagorean Theorem Converse)

4, 5, 6

• Yes

• No

Answer explanation

$4^2+5^2=6^2\ ?$
$16+25=36\ ?$
$41\ne36$
The left and right side of the equation are not equal, so these side lengths do not form a right triangle.

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CCSS.HSG.SRT.B.4

CCSS.HSG.SRT.C.8

Isabella has sticks that are 10cm, 11cm, and 13cm long.  Can she place the sticks together to form a right triangle?  Justify your answer.

• No, because 10+11 does not equal 13
• No, because 100+121 does not equal 169
• Yes, because there is a small side, medium side and long side
• Yes, because a triangle has 3 sides

Tags

CCSS.HSG.SRT.C.8