Similar Triangles and Proportions

The video tutorial explains how to find the value of x, which is a leg of a smaller right triangle. It demonstrates that the larger triangle is similar to the smaller one, allowing the use of proportions to solve for x. The tutorial sets up a proportion, cross-multiplies, and solves the resulting equation to find x equals 5. The process includes verifying the solution through mental math and algebraic steps.

What is the unknown variable x in the problem?

• The hypotenuse of the larger triangle

• The distance between two points in the smaller triangle

• The perimeter of the smaller triangle

• The area of the larger triangle

Why are the two triangles considered similar?

• They have equal angles

• They have the same perimeter

• They have the same area

• They have proportional corresponding sides

What is the first step in setting up the proportion?

• Identify the hypotenuse of the larger triangle

• Compare the corresponding sides of the triangles

• Calculate the area of the smaller triangle

• Find the perimeter of the larger triangle

What should be written on the bottom of the proportion?

• The sum of 10 and x

• The length of the smaller triangle's hypotenuse

• The difference between 10 and x

• The length of the larger triangle's base

What is the result of cross-multiplying the proportion?

• 10x equals 2 times the sum of 6 plus x

• 6x equals 2 times the sum of 10 plus x

• x equals 10 times the sum of 6 plus 2

• 2x equals 6 times the sum of 10 plus x

What is the next step after setting up the equation 6x = 2(10 + x)?

• Multiply both sides by 2

• Subtract 2x from both sides

• Add 2x to both sides

• Divide both sides by 6

What is the value of x after solving the equation?

• 7

• 6

• 5

• 4

Which property is used to distribute 2 in the equation 2(10 + x)?

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

What operation is performed to isolate x in the equation 4x = 20?

• Division

• Multiplication

• Subtraction

• Addition

What is the purpose of setting up a proportion in this problem?

• To solve for the unknown variable x

• To find the area of the triangles

• To compare the angles of the triangles

• To determine the perimeter of the triangles