Side-Splitter Theorem

Front

What is the Side-Splitter Theorem?

Back

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

Front

If DE is parallel to BC in triangle ABC, and AD/DB = DE/BC, what does this imply?

Back

This implies that the segments AD and DB are proportional to the segments DE and BC.

Front

In triangle ABC, if AD = 3, DB = 2, and DE = 6, how do you find BC?

Back

Use the proportion: AD/DB = DE/BC. Substitute the values: 3/2 = 6/BC, then solve for BC.

Front

What is the formula to find the length of a segment when using the Side-Splitter Theorem?

Back

The formula is: (AD/DB) = (DE/BC).

Front

If a triangle has sides of lengths 3, 2, and a segment DE of length 6, what is the length of BC?

Back

BC = 4, calculated using the proportion from the Side-Splitter Theorem.

Front

What does it mean for two lines to be parallel in the context of triangles?

Back

Parallel lines in triangles create proportional segments on the other sides of the triangle.

Front

If CB = 3, CA = 10, and CE = 6 in triangle ACT, how do you find ET?

Back

Use the proportion: CB/CA = CE/ET. Substitute the values and solve for ET.

Front

What is the significance of the Side-Splitter Theorem in geometry?

Back

It helps in solving problems involving similar triangles and finding unknown lengths.

Front

If AD = 3 and DB = 2, what is the ratio of AD to DB?

Back

The ratio is 3:2.

Front

How can you determine if two triangles are similar using the Side-Splitter Theorem?

Back

If the corresponding sides are proportional, the triangles are similar.