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

Back

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

Front

How do you set up a proportion using the Side-Splitter Theorem?

Back

If a line segment divides sides a and b of a triangle, and the segment is parallel to side c, then the proportion can be set up as a/b = d/e, where d and e are the segments created on the sides.

Front

What is the formula to find the missing length using the Side-Splitter Theorem?

Back

If a/b = c/d, then ad = bc, allowing you to solve for the missing length.

Front

If a triangle has sides of lengths 15 and 7, and a line segment divides them into lengths of x and 14, what proportion should you use?

Back

x / 15 = 7 / 14.

Front

What is the value of x if 15 / x = 7 / 14?

Back

x = 15 * (14 / 7) = 30.

Front

If a triangle has a side of length 10 and is divided by a parallel line into segments of lengths 4 and x, what is the value of x?

Back

Using the proportion 4 / 10 = x / 15, we find x = 6.

Front

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

Back

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

Front

If a triangle has sides of lengths 12 and 8, and a line segment divides them into lengths of 6 and x, what is the value of x?

Back

Using the proportion 6 / 12 = x / 8, we find x = 4.

Front

What is the relationship between similar triangles and the Side-Splitter Theorem?

Back

The Side-Splitter Theorem is used to prove that triangles formed by a parallel line are similar to the original triangle.