Proportions and the Side Splitter Theorem

The video tutorial explains the Side Splitter Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. The tutorial demonstrates how to set up and solve proportions using this theorem, including substituting values and solving for variables using cross products.

What does the Side Splitter Theorem state?

• A line parallel to one side of a triangle divides the triangle into two equal areas.

• A line parallel to one side of a triangle does not affect the other sides.

• A line parallel to one side of a triangle divides the other two sides proportionally.

• A line parallel to one side of a triangle divides the other two sides equally.

If a line is parallel to one side of a triangle, what does it do to the other two sides?

• It does not affect them.

• It divides them proportionally.

• It divides them into two equal parts.

• It makes them equal in length.

Which segments are divided proportionally by the line in the triangle?

• AN and DM

• DM and MC, AN and NC

• DM and AN

• MC and NC

How is the proportion between segments DM, MC, AN, and NC expressed?

• DM/NC = AN/MC

• DM/MC = NC/AN

• DM/MC = AN/NC

• DM/AN = MC/NC

What is the first step in setting up the geometric proportion?

• Draw the triangle.

• Identify the parallel line.

• Calculate the length of the segments.

• Write the proportion using segment measures.

What values are substituted into the proportion for BM and MC?

• BM = 10, MC = 6

• BM = 10, MC = 12

• BM = 6, MC = 12

• BM = 12, MC = 6

What is the value of AN in the proportion?

• 12

• 7.2

• 10

• 6

What mathematical operation is used to solve the equation for the variable?

• Addition

• Subtraction

• Division

• Cross multiplication

What is the result of the cross multiplication in the equation?

• 12y = 60

• 10y = 60

• 10y = 72

• 12y = 72

What is the purpose of using cross products in solving the equation?

• To check the accuracy of the proportion

• To simplify the equation

• To find the length of the triangle sides

• To solve for the variable