Triangle Ratios and Properties

The video tutorial explains how to solve a geometry problem involving a large triangle with two smaller, similar triangles inside it. The instructor demonstrates how to set up and solve a ratio equation to find the missing side length, x, using the properties of similar triangles and the distributive property. The solution involves setting up a proportion, cross-multiplying, and simplifying the equation to find the value of x.

What is the first step in solving the problem involving the triangles?

• Create a ratio

• Identify the type of triangles

• Measure the angles

• Calculate the area

Why are the two triangles inside the bigger triangle considered similar?

• They have the same area

• They have the same angles

• They have the same perimeter

• They have the same height

How do you express the ratio of the sides of the smaller triangle to the bigger triangle?

• As a sum

• As a product

• As a fraction

• As a difference

What is the ratio of the side 5 of the smaller triangle to the corresponding side of the bigger triangle?

• x/5

• 10/5

• 5/10

• 5/x

How do you find the unknown side of the triangle if the entire side is 10 and a part of it is x?

• 10 * x

• x - 10

• 10 - x

• 10 + x

What is the next step after setting up the ratio and determining the unknown side?

• Add the ratios

• Cross-multiply

• Subtract the ratios

• Divide the ratios

What is the result of cross-multiplying 7 and x?

• 7+x

• x7

• x-7

• 7x

What property is used when multiplying 5 to both 10 and -x?

• Distributive property

• Associative property

• Identity property

• Commutative property

What is the simplified form of 50 over 12?

• 12/25

• 25/3

• 25/6

• 50/6

What is the final value of x?

• 25/6

• 7x

• 10

• 50/12