Triangle Proportionality and Ratios

The video tutorial covers the triangle proportionality theorem and its converse, illustrating both with diagrams and exercises. It explains how to solve problems using these theorems and explores different methods for solving proportions in triangles. The tutorial concludes with a proof of the triangle proportionality theorem using algebraic methods.

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

• The line bisects the triangle into two equal areas.

• The line divides the other two sides proportionally.

• The line creates two congruent triangles.

• The line is perpendicular to the base.

When solving for a missing side using the Triangle Proportionality Theorem, what is a common method used?

• Finding the area of the triangle.

• Using the Pythagorean theorem.

• Cross-multiplying the known ratios.

• Calculating the perimeter of the triangle.

What is the outcome when the proportion 14:12 is compared to X:18?

• The missing side is 21.

• The missing side is 12.

• The missing side is 18.

• The missing side is 9.

What is the outcome when the proportion 6:2 is compared to 18:6?

• The missing side is 21.

• The missing side is 18.

• The missing side is 12.

• The missing side is 9.

What is the result when the proportion 12:4 is compared to Z:3?

• The missing side is 21.

• The missing side is 18.

• The missing side is 12.

• The missing side is 9.

What is the outcome when the proportion 14:12 is compared to X:18?

• The missing side is 9.

• The missing side is 12.

• The missing side is 18.

• The missing side is 21.

What is the outcome when the proportion 6:2 is compared to 18:6?

• The missing side is 21.

• The missing side is 12.

• The missing side is 9.

• The missing side is 18.

In the Converse of the Triangle Proportionality Theorem, what must be true for the line to be parallel to one side of the triangle?

• The line must divide the other two sides proportionally.

• The line must create two congruent triangles.

• The line must be the same length as the base.

• The line must be perpendicular to the base.

What is the result when the proportion 18:10 is compared to 24:15?

• The lines are parallel.

• The lines are not parallel.

• The triangles are congruent.

• The triangles are similar.

What is the outcome when the proportion 22.5:25 is compared to 18:20?

• The triangles are similar.

• The triangles are congruent.

• The lines are not parallel.

• The lines are parallel.