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

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

Back

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

Front

In triangle ABC, if DE is parallel to BC and D is on AB while E is on AC, what is the relationship between AD/DB and AE/EC?

Back

AD/DB = AE/EC.

Front

How can the Triangle Proportionality Theorem be used to find unknown lengths in a triangle?

Back

By setting up a proportion based on the segments created by the parallel line and solving for the unknown length.

Front

If AD = 3, DB = 6, AE = 4, what is the length of EC using the Triangle Proportionality Theorem?

Back

EC = 8 (Using the proportion AD/DB = AE/EC, we have 3/6 = 4/x, solving gives x = 8).

Front

What is the converse of the Triangle Proportionality Theorem?

Back

The converse states that 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 5, 12, and 13, is it a right triangle?

Back

Yes, because 5^2 + 12^2 = 13^2.

Front

What is the significance of similar triangles in relation to the Triangle Proportionality Theorem?

Back

Similar triangles have corresponding sides that are proportional, which is a key aspect of the Triangle Proportionality Theorem.

Front

If two triangles are similar, how do their corresponding sides relate?

Back

The ratios of the lengths of corresponding sides are equal.

Front

In triangle XYZ, if XY = 10, XZ = 15, and YZ = 12, are the triangles similar to triangle ABC with sides 5, 8, and 6?

Back

No, because the ratios of the sides are not equal.