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 triangle has sides of lengths 6 and 8, and a line parallel to the base divides the other two sides, what is the ratio of the segments?

Back

The ratio of the segments is 6:8 or 3:4.

Front

How do you find the missing length using the Side-Splitter Theorem?

Back

To find the missing length, set up a proportion based on the lengths of the segments created by the parallel line.

Front

If a triangle has a base of 10 and a parallel line divides the other two sides into segments of 4 and x, what is x?

Back

x = (10 * 4) / 6 = 6.67.

Front

What is the relationship between the segments created by a parallel line in a triangle?

Back

The segments are proportional to the lengths of the sides of the triangle.

Front

If a triangle has sides of lengths 12 and 16, and a line parallel to the base divides the other two sides into segments of 3 and x, what is x?

Back

x = (16 * 3) / 12 = 4.

Front

What is the formula for the Side-Splitter Theorem?

Back

If a line parallel to one side of a triangle intersects the other two sides, then a/b = c/d, where a and b are segments on one side and c and d are segments on the other.

Front

If a triangle has a base of 14 and a parallel line divides the other two sides into segments of 7 and x, what is x?

Back

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

Front

What does it mean for two segments to be proportional?

Back

Two segments are proportional if the ratio of their lengths is equal.

Front

If a triangle has sides of lengths 18 and 24, and a line parallel to the base divides the other two sides into segments of 9 and x, what is x?

Back

x = (24 * 9) / 18 = 12.