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 10 and 20, 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 1:2.

Front

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

Back

To set up a proportion, use the lengths of the divided segments on the two sides of the triangle and set them equal to each other.

Front

If x/10 = 15/30, what is the value of x?

Back

x = 5.

Front

What is the first step in solving a problem using the Side-Splitter Theorem?

Back

Identify the parallel line and the segments it creates on the triangle.

Front

If a triangle has sides of lengths 15 and 45, and a line parallel to the base divides the other two sides, what is the length of the segment created on the shorter side if the longer side is 30?

Back

The length of the segment on the shorter side is 10.

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 other two sides of the triangle.

Front

If a triangle has a base of 30 and a height of 20, what is the area of the triangle?

Back

Area = 1/2 * base * height = 1/2 * 30 * 20 = 300.

Front

In the proportion x/10 = 15/30, what does the 10 represent?

Back

The 10 represents the length of the segment on the side of the triangle that is not divided by the parallel line.

Front

If a triangle's sides are divided into segments of lengths 4 and 8, what is the ratio of the segments?

Back

The ratio of the segments is 1:2.