Properties and Theorems of 45-45-90 Triangles

The video tutorial explains how to derive a 45-45-90 special right triangle from a square. It begins by setting up a square with equal sides and angles, then cuts the square diagonally to form two 45-45-90 triangles. The tutorial analyzes the angles and sides, using the Pythagorean theorem to calculate the hypotenuse. It concludes by highlighting the side ratios of 1:1:√2 for the 45-45-90 triangle.

What is the first step in constructing a 45-45-90 triangle?

• Start with a triangle

• Start with a rectangle

• Start with a square

• Start with a circle

What is true about the sides of a square?

• All sides are different lengths

• Two sides are equal, two are different

• All sides are equal

• Only opposite sides are equal

How do you form a 45-45-90 triangle from a square?

• Cut the square diagonally

• Cut the square vertically

• Cut the square into four parts

• Cut the square horizontally

What is the measure of each angle in a 45-45-90 triangle?

• 90, 90, 90 degrees

• 60, 60, 60 degrees

• 45, 45, 90 degrees

• 30, 60, 90 degrees

What happens to the angles when a square is divided diagonally?

• They become 45 degrees

• They become 60 degrees

• They become 30 degrees

• They remain 90 degrees

What are the known side lengths of the triangle after redrawing?

• 1 and 2

• 1 and 1

• 2 and 2

• 1 and 3

Which theorem is used to find the hypotenuse of the triangle?

• Pythagorean theorem

• Thales' theorem

• Sine rule

• Cosine rule

What is the formula for the Pythagorean theorem?

• a + b = c

• a^2 - b^2 = c^2

• a^2 + b^2 = c

• a^2 + b^2 = c^2

What is the first step in using the Pythagorean theorem?

• Identify the hypotenuse

• Identify the area

• Identify the angles

• Identify the legs

What is the result of 1 squared plus 1 squared?

• 1

• 2

• 3

• 4