Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the triangle proportionality theorem, explaining how a line parallel to one side of a triangle divides the other two sides proportionally. It includes examples of solving for unknowns using cross-multiplication and explores the converse of the theorem. The tutorial also addresses working with expressions in proportions and determining if lines are parallel using the theorem. Finally, it discusses proportional parts with parallel lines, extending the concept beyond triangles.

What does the Triangle Proportionality Theorem state?

• If a line is parallel to one side of a triangle, it divides the other two sides proportionally.

• If a line is perpendicular to one side of a triangle, it divides the other two sides proportionally.

• If a line bisects one side of a triangle, it divides the other two sides proportionally.

• If a line is parallel to one side of a triangle, it divides the other two sides equally.

In the converse of the Triangle Proportionality Theorem, what can be concluded if BD/DA = BE/EC?

• DE is perpendicular to AC.

• DE is parallel to AC.

• DE bisects AC.

• DE is equal to AC.

Given that DE is parallel to AC, if BD = 14, DA = 12, and BE = x, EC = 15, what is the value of x?

• 17.5

• 18

• 16.5

• 15.5

If DE is parallel to AC and BD/DA = BE/EC, with BD = x, DA = 18, BE = 56, and EC = 21, what is x?

• 54

• 48

• 50

• 52

For a triangle with DE parallel to AC, if the whole side is 55 and a segment is 45, what is the length of the missing segment?

• 10

• 15

• 20

• 25

If DE is parallel to AC and the whole side is 27 with a segment of 6, what is the length of the missing segment?

• 24

• 22

• 21

• 23

Given DE parallel to AC, if 30/(x+7) = 25/15, what is the value of x?

• 14

• 11

• 12

• 13

If DE is parallel to AC and 6/21 = (x-1)/(3x+1), what is the value of x?

• 9

• 10

• 12

• 11

If three parallel lines intersect two transversals, and the segments are 45, 18, 52, and x, what is x?

• 22.8

• 21.8

• 20.8

• 23.8

For three parallel lines intersecting two transversals, if 24/18 = (3x+1)/12, what is the value of x?

• 8

• 6

• 5

• 7