Triangles and Squares: Properties and Relationships

The video tutorial covers the properties and calculations related to 45-45-90 triangles, including their similarity and use in determining the diagonal of a square. It also discusses safe angles for biking using triangle ratios, finding missing lengths with similarity and the Pythagorean theorem, and the properties of isosceles and equilateral triangles.

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

• 30°, 60°, 90°

• 45°, 45°, 90°

• 90°, 90°, 90°

• 60°, 60°, 60°

In a 45-45-90 triangle, if one leg is 1, what is the length of the hypotenuse?

• 2

• √3

• √2

• 1

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

• Divide by √2

• Divide by 2

• Multiply by 2

• Multiply by √2

What is the diagonal of a square with side length 1?

• 2

• √2

• 1

• √3

If the diagonal of a square is 5 cm, what is the area of the square?

• 15 cm²

• 10 cm²

• 25 cm²

• 12.5 cm²

What is the ratio of the legs in a right triangle with a 7° angle?

• 1:2

• 1:√2

• 1:1

• 3:25

Which method can be used to find missing lengths in right triangles?

• Similarity

• Pythagorean Theorem

• Both

• Neither

In a right triangle, if the hypotenuse is 25 and one leg is 24, what is the length of the other leg?

• 9

• 15

• 12

• 7

Are all isosceles triangles similar?

• Yes

• No

• Sometimes

• Only if they are equilateral

Are all equilateral triangles similar?

• Sometimes

• Only if they have the same side length

• Yes

• No