Triangle Proportionality and Segment Lengths

This video tutorial covers solving for unknown values using the triangle proportionality theorem. It begins with a review of the theorem, explaining how a parallel line to one side of a triangle divides the other two sides proportionally. The video then provides two examples: the first involves finding the length of segment BC, and the second involves finding the lengths of segments AC, BD, DC, and DE. Each example demonstrates setting up proportions and solving for unknowns using cross-multiplication.

What is the triangle proportionality theorem primarily concerned with?

• The angles of a triangle

• The proportional division of sides by a parallel line

• The area of a triangle

• The perimeter of a triangle

What happens when a parallel line intersects two sides of a triangle?

• It divides the sides proportionally

• It forms a right angle

• It creates equal angles

• It bisects the triangle

In the first example, what is the length of segment BC if BE is parallel to CD?

• 15 units

• 8 units

• 12 units

• 10 units

In the second example, what is the combined length of segment AC?

• 27 units

• 45 units

• 36 units

• 18 units

How is the length of segment BD determined in the second example?

• By using a proportion with BC and AC

• By measuring directly

• By adding the lengths of AC and DC

• By subtracting the length of DE from AC

What is the length of segment BD in the second example?

• 14.4 units

• 21.6 units

• 16.8 units

• 18 units

What is the length of segment DC in the second example?

• 14.4 units

• 21.6 units

• 18 units

• 16.8 units

Which proportion could also be used to find the length of DC?

• y to 28 must equal 18 to 45

• y to 36 must equal 27 to 45

• y to 18 must equal 27 to 36

• y to 45 must equal 36 to 27

What is the length of segment DE in the second example?

• 14.4 units

• 18 units

• 21.6 units

• 16.8 units

What concept is emphasized in the conclusion of the video?

• The use of similar triangles and proportions

• The division of triangles into smaller parts

• The calculation of triangle areas

• The measurement of angles