12.1 Triangle Proportionality Theorem

Front

What is the Triangle Proportionality Theorem?

Back

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

How do you determine if two segments are parallel in a triangle?

Back

To determine if two segments are parallel, you can use the Triangle Proportionality Theorem or check if corresponding angles are equal.

Front

What is the significance of parallel lines in triangles?

Back

Parallel lines in triangles help establish proportional relationships between the sides of the triangle, which can be used to solve for unknown lengths.

Front

If a line segment divides two sides of a triangle proportionally, what can be concluded about the line segment?

Back

The line segment is parallel to the third side of the triangle.

Front

What is the formula for finding the length of a side in a triangle using the Triangle Proportionality Theorem?

Back

If a line divides two sides of a triangle, the lengths of the segments can be expressed as a/b = c/d, where a and b are segments on one side, and c and d are segments on the other side.

Front

How can you apply the Triangle Proportionality Theorem to solve for unknown lengths?

Back

Set up a proportion using the known lengths and solve for the unknown variable.

Front

What is the relationship between the angles formed by a transversal intersecting parallel lines?

Back

The angles formed by a transversal intersecting parallel lines are either equal (corresponding angles) or supplementary (consecutive interior angles).

Front

What does it mean if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you prove that two triangles are similar using the Triangle Proportionality Theorem?

Back

If a line parallel to one side of a triangle intersects the other two sides, it creates two smaller triangles that are similar to the original triangle.

Front

What is the importance of the concept of proportionality in geometry?

Back

Proportionality allows for the comparison of lengths and areas, enabling the solution of various geometric problems.