Topic 9-4

Topic 9-4

45-45-90 Triangles

Right Triangles

Methods to use

Pythagorean Theorem: a² + b² = c²

GOING TO LOOK ANOTHER METHOD OF A SPECIAL RIGHT TRIANGLE

 $45\degree-45\degree-90\degree\ triangles$  

 $x\ -x\ -\ x\sqrt{2}$  

Multiple Choice

Find a.

• 5

• √2

• 5√2

• 2

Multiple Choice

What is the length of y in this picture?

• 45
• 5√2
• 90
• 5

Multiple Choice

• a=4 b=2√2

• a=2√2 b=2√2

• a=2√2 b=4

• a=4 b=4

Multiple Choice

What is the length of y in this 45-45-90 triangle?

• 8√2
• 4√2
• 4
• 8

Multiple Choice

Sam's square bedroom has a diagonal of 9√2 feet. What is the length of each side?

• 18

• 3√2

• 9

• 12.7

Multiple Choice

A square has a perimeter of 32 inches. What is the length of the diagonal?

• 16

• 4√2 in

• 32√2 in

• 8√2 in

Multiple Choice

Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45∘.

• 4 inches

• 2 inches

• 8 inches

• 10 inches

Multiple Choice

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

• Multiply that leg by 2
• Use the same length for the second leg
• Multiply that leg by √2

Multiple Choice

Find the length of the diagonal of a square with side length 12 cm.

• 12√2 cm
• 6√2 cm
• 7√2 cm
• 13
  13√2 cm

Multiple Choice

If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.

• 7√2
• 49√2
• 7
• 7√7

Multiple Choice

Find a - the length of the hypotenuse.

• 2√6
• 2√3
• 3
• 6

Multiple Choice

Find a - the length of a leg of the triangle.

• 4
• 2
• 4√2
• 2√4

Multiple Choice

What is the value of x?

• 12√2

• 2√12

• 24

• 2

Multiple Choice

Find the value of x.

• 3 sqrt(2)

• 3

• 6 sqrt(2)

• 6

Multiple Choice

Solve for a and b in the special right triangle.

• a = 5, b = 5

• a = 10, b = 10√2

• a = 10√2, b = 10√2

• a = 5√2, b = 5√2

Multiple Choice

Use the 45-45-90 theorem to solve for the hypotenuse.

• 16

• 8

• 8√2

• √16

Multiple Choice

Find the missing side lengths.

• a = 4, b = 4

• a = 4, b = 2√2

• a = 2√2, b = 4

• a = 4, b = 4

Multiple Choice

What is the value of x?

• 2

• 18

• 2√9

• 9√2

Multiple Choice

Find the value of y.

• 11√2

• 11

• 22

• (11√2)/2

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2

• 4

• 8

• 4√3