Exploring 45-45-90 Triangle Properties

The video tutorial covers the 45-45-90 triangle, a crucial concept in geometry and frequently tested on the SAT. It explains the properties and classification of this triangle, including its congruent angles and equal legs. The tutorial demonstrates solving these triangles using the Pythagorean theorem and explores advanced examples with simplification techniques. It also applies the knowledge to squares and diagonals, emphasizing the practical application of these concepts. The session concludes with a discussion on real-world applications, reinforcing the importance of understanding the 45-45-90 triangle.

What is the significance of the 45-45-90 triangle in geometry?

• It is the simplest form of a right triangle.

• It appears frequently on standardized tests like the SAT.

• It cannot be solved using the Pythagorean theorem.

• It is the only triangle with three equal sides.

What type of triangle is a 45-45-90 triangle?

• Equilateral

• Isosceles

• Scalene

• Obtuse

What is the relationship between the legs of a 45-45-90 triangle?

• One leg is twice as long as the other.

• They are of equal length.

• They have different lengths.

• They are perpendicular.

What formula is used to solve for the hypotenuse in a right triangle?

• 2a + 2b = c

• a + b = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

How can you solve for the hypotenuse of a 45-45-90 triangle if the legs are known?

• Multiply one leg by the square root of 2.

• Use the Pythagorean theorem.

• Divide the length of one leg by 2.

• Add the lengths of the legs.

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

• Divide the hypotenuse by the square root of 2.

• Multiply the hypotenuse by the square root of 2.

• Divide the hypotenuse by 2.

• Square the hypotenuse.

In a 45-45-90 triangle, if one leg is 5 units, what is the length of the hypotenuse?

• 7.5 units

• 10 units

• 5 square root of 2 units

• 5 units

If the hypotenuse of a 45-45-90 triangle is 10√2, what is the length of one leg?

• 5√2 units

• 5 units

• 10 units

• 10√2 units

How do you check if your solution for the sides of a 45-45-90 triangle is correct?

• Divide the hypotenuse by the square root of 2.

• Multiply the sides by 2.

• Compare it to another triangle.

• Use the Pythagorean theorem.

What is the area of a square if its diagonal is 2√5 units?

• 5 units squared

• 10 units squared

• 20 units squared

• 25 units squared