Triangle Proportionality and Proportions

The video tutorial covers the triangle proportionality theorem, also known as the side splitter theorem. It explains how a line parallel to one side of a triangle divides the other two sides into proportional segments. The tutorial includes multiple examples demonstrating how to set up and solve proportions using this theorem. It also covers the concept of parallel lines and proportional parts, providing practice problems for students to solve on their own. The video concludes with a summary and additional resources for further learning.

What does the Triangle Proportionality Theorem state about a line parallel to one side of a triangle?

• It makes the triangle an isosceles triangle.

• It divides the other two sides into segments of proportional lengths.

• It creates segments of equal length on the other two sides.

• It divides the triangle into two equal areas.

In the first example, what is the value of x when the proportion 12/(x+1) = 9/x is solved?

• x = 4

• x = 3

• x = 5

• x = 2

How can you verify your solution when using the Triangle Proportionality Theorem?

• By checking if the triangle is equilateral.

• By ensuring the calculated segments are equal.

• By plugging the value back into the original proportion and simplifying.

• By measuring the angles of the triangle.

In the second example, what is the length of site c when using the proportion 8/7.2 = 6.4/c?

• c = 6.00

• c = 5.76

• c = 8.00

• c = 7.20

What is the result of solving the proportion x/36 = 10/45?

• x = 6

• x = 9

• x = 7

• x = 8

What is the concept of parallel lines and proportional parts?

• Parallel lines create equal angles with transversals.

• Parallel lines divide transversals into equal segments.

• Parallel lines intersecting transversals create proportional segments.

• Parallel lines make all triangles similar.

If three parallel lines intersect two transversals, what is the relationship between the segments they create?

• The segments are congruent.

• The segments form a right angle.

• The segments are proportional.

• The segments are equal in length.

In the exercise, what is the value of x when using the proportion 45/18 = 52/x?

• x = 22.5

• x = 20.8

• x = 18.4

• x = 24.0

How do you find the missing segment when given the entire length and a part of it?

• Add the known part to the entire length.

• Multiply the known part by the entire length.

• Subtract the known part from the entire length.

• Divide the known part by the entire length.

What is the value of x when solving the proportion 27/x = 18/14?

• x = 20

• x = 22

• x = 21

• x = 19