Pythagorean Theorem and Perimeter

Pythagorean Theorem Introduction

Dr. Tom Giles

Multiple Choice

What is the Pythagorean Theorem?

• $$a^2+b^2=c^2$$

• There is really only one real option here.

Multiple Choice

What must be true in order for the Pythagorean Theorem to work?

• The triangle must be right.

• The triangle must be isoceles.

• It works every time.

Multiple Select

Which side on a right triangle is ALWAYS the longest side

• the side opposite the right angle

• Hypotenuse

Multiple Choice

_{^{Find the missing side}}

• 9
• 41
• 6.4
• 3

Multiple Choice

a² + b² = c^{2
a = 9 b = 40}

• c = 41
• c = 65
• c = 25
• c = 5

Multiple Choice

a² + b² = c^{2
b = 35 c = 37}

• a = 12
• a = 11
• a = 18
• a = 14

Multiple Choice

Which side is could we use for c?

• 24

• 25

• 7

• Any of them

Multiple Choice

Which side could we use for a?

• 24

• Any of them

• 7

• 7 or 24

Multiple Choice

Find the length of the missing side. 

• 25 cm
• 42 cm
• 52 cm
• 48 cm

Multiple Choice

What is the longest side of a right triangle called?

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

Multiple Choice

They Hypotenuse of a right triangle is the side across from the:

• Right Angle

• Smallest Angle

• Acute Angle

• Hypo Angle

Multiple Choice

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Multiple Choice

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet
• 26 feet
• 27 feet
• 28 feet

Multiple Choice

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

Multiple Choice

Find the missing side.

Round your answer to the nearest tenth place.

• 11.5 ft

• 11 ft

• 12 ft

• 15.6 ft

Multiple Choice

The size of a television screen is measured by the length of the diagonal of the screen.  What size is a television screen that is 3 feet tall and 6 feet wide?

• 18
• 6.7

Multiple Choice

Find the hypotenuse in the image shown

• 15 cm

• 20 cm

• 10 cm

• 9 cm

Multiple Choice

Find the perimeter of a triangle that has legs that are 3 cm and 4 cm. 

• 5
• 7
• 10
• 12

Multiple Choice

How far did Joshua swim across the pool?

• G
• O
• E
• X

Multiple Choice

Use the Pythagorean Theorem to find the length of side x

• x = 14.3

• x = 15.3

• x = 16.3

• x = 17.3

Multiple Choice

What is the length of the unknown side?

• 32 in.

• 68 in.

• 40 in.

• 80 in.

​If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse.

​When the sum of Leg Sides ≠ Square of Hypotenuse

Multiple Choice

Can a right triangle have sides of length

5, 12, and 13?

• Yes.

• No.

Multiple Choice

Can a right triangle have sides of length

3, 6, and 9

• yes

• no

Multiple Choice

What type of triangle would have side lengths of

3, 6, and 9

• Acute

• Obtuse

Multiple Choice

State if the three sides lengths form an acute, obtuse, or right triangle:
7 in, 11 in, 13 in

• acute
• obtuse
• right