12.1 Triangle Proportionality Theorem

Front

What is the Triangle Proportionality Theorem?

Back

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

Front

What does the Converse of the Triangle Proportionality Theorem state?

Back

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle.

Front

If line segment AB is parallel to line segment CD, and they are cut by a transversal, what can be said about the angles formed?

Back

The corresponding angles are equal.

Front

In a triangle, if segment DE is parallel to segment FG, and DE divides the sides of triangle ABC proportionally, what can we conclude?

Back

DE is parallel to FG by the Triangle Proportionality Theorem.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The corresponding sides are in proportion.

Front

What is the relationship between the ratios of the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides are equal.

Front

If a triangle has sides of lengths 6, 8, and 10, what can be concluded about its angles?

Back

It is a right triangle because it follows the Pythagorean theorem.

Front

How do you find the length of a side in a triangle using the Triangle Proportionality Theorem?

Back

Set up a proportion based on the lengths of the sides that are divided by the parallel line.

Front

If segment XY is parallel to segment ZW and divides the triangle into two smaller triangles, what can be said about the areas of these triangles?

Back

The areas of the triangles are proportional to the lengths of the corresponding sides.