Triangle Proportionality Theorems and Applications

The video tutorial covers the two transversal proportionality corollary, explaining how three or more parallel lines intersecting two transversals divide the transversals proportionally. It recaps the triangle proportionality theorem and applies the corollary to real-world examples, such as a tree line street and a Manhattan street map. The lesson concludes with a preview of the next topic, the triangle bisector theorem.

What is a corollary in mathematical terms?

• A hypothesis that cannot be proven

• A theorem that is proven independently

• A theorem whose proof follows directly from another theorem

• A statement that contradicts a theorem

What does the Triangle Proportionality Theorem state?

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

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

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

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

In the Triangle Proportionality Theorem, what happens if the line is not parallel?

• The sides are divided proportionally

• The sides are not divided proportionally

• The triangle becomes a square

• The sides are divided equally

What does the Two Transversal Proportionality Corollary state?

• Three or more parallel lines divide two transversals equally

• Two transversals divide three or more parallel lines proportionally

• Three or more parallel lines divide two transversals proportionally

• Two transversals divide three or more parallel lines equally

In the tree-lined street example, what is the relationship between the segments?

• Segments are proportional if lines are perpendicular

• Segments are proportional if lines are parallel

• Segments are unrelated

• Segments are equal in length

How is the segment addition postulate used in the tree-lined street example?

• To divide the lengths of segments proportionally

• To add the lengths of non-parallel segments

• To subtract the lengths of parallel segments

• To add the lengths of segments to find a total length

In the Manhattan map example, what are the transversals?

• Broadway and Avenue of the Americas

• 34th, 35th, and 36th streets

• Central Park and Times Square

• 5th Avenue and Madison Avenue

What is the approximate length found between 34th and 35th street along Broadway?

• 250 feet

• 275 feet

• 286 feet

• 300 feet

What is the next topic after the Two Transversal Proportionality Corollary?

• Similarity and Congruence

• Pythagorean Theorem

• Triangle Bisector Theorem

• Triangle Proportionality Theorem