Right Triangles Pythagorean Theorem and Converse

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.

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

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

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.

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

A ladder is leaning against a building. The base of the ladder is 5 feet from the building, and the top of the ladder reaches 10 feet high on the building.
What is the length of the ladder, rounded to the nearest foot?

• 9 feet

• 11 feet

• 13 feet

• 15 feet

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

Of these 4 numbers, 3 will form a right triangle. Which number is not used?

• 7

• 20

• 24

• 25

Which set of side lengths does not form a right triangle?

• 38, 80, 90

• 16, 63, 65

• 36, 77, 85

• 14, 15, 29

A piece of paper that SaVanna has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

• 7.5 in

• 12.4 in

• 13.6 in

• 14.3 in

Which set of side lengths form a right triangle?

• 3, 4, 7

• 33, 56, 65

• 66, 72, 97

• 10, 15, 25