Understanding Special Right Triangles

The video tutorial explains the properties and side ratios of 30-60-90 and 45-45-90 triangles. It begins with a review of 30-60-90 triangles, detailing how the sides relate to each other. The tutorial then introduces 45-45-90 triangles, explaining that they are right isosceles triangles with equal legs. Using the Pythagorean theorem, the video derives the side ratios for 45-45-90 triangles, showing that the hypotenuse is the square root of 2 times the length of a leg. The video concludes with a comparison of the two triangle types and their respective side ratios.

What is the ratio of the sides in a 30-60-90 triangle if the shortest side is 1?

• 1:2:3

• 1:√3:2

• 1:1:√2

• 1:√2:3

Tags

CCSS.HSG.CO.C.10

If a triangle has sides in the ratio 1:√3:2, what type of triangle is it?

• Scalene Triangle

• 30-60-90 Triangle

• 45-45-90 Triangle

• Equilateral Triangle

Tags

CCSS.HSG.CO.C.10

How can you identify a 30-60-90 triangle based on its side lengths?

• The sides are in the ratio 1:1:√2

• The sides are in the ratio 1:√3:2

• The sides are in the ratio 2:2:2

• All sides are equal

Tags

CCSS.HSG.CO.C.10

What is a 45-45-90 triangle also known as?

• Right Isosceles Triangle

• Equilateral Triangle

• Acute Triangle

• Scalene Triangle

Tags

CCSS.HSG.CO.C.10

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

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

Tags

CCSS.8.G.B.8

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

• 2x

• x√2

• x/2

• x

Tags

CCSS.8.G.B.8

Which theorem is used to derive the side ratios of a 45-45-90 triangle?

• Area Theorem

• Cosine Rule

• Sine Rule

• Pythagorean Theorem

Tags

CCSS.8.G.B.8

If a 45-45-90 triangle has a leg of length 3, what is the length of the hypotenuse?

• 3

• 3√2

• 3/2

• 6

Tags

CCSS.8.G.B.8

In a 45-45-90 triangle, what is the ratio of the legs to the hypotenuse?

• 1:2:3

• 1:1:2

• 1:√3:2

• 1:1:√2

Tags

CCSS.8.G.B.8

What is the hypotenuse of a 45-45-90 triangle if one leg is 5?

• 5/2

• 10

• 5√2

• 5

Tags

CCSS.8.G.B.8