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 15, 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 the same as the ratio of the sides, which is 10:15 or 2:3.

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 and the corresponding sides of the triangle.

Front

If a triangle has a side of length 10 and a corresponding segment of length x, what is the proportion if the other side is 30?

Back

The proportion is x/10 = 30/15.

Front

What is the first step in solving for x using the Side-Splitter Theorem?

Back

Identify the corresponding sides and set up the proportion.

Front

If a triangle's sides are divided into segments of lengths 4 and x, and the corresponding sides are 8 and 12, what is x?

Back

x = 6, using the proportion 4/x = 8/12.

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

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

Back

Check if the ratios of the lengths of the corresponding sides are equal.

Front

If a triangle has a base of 20 and a segment of length 10, what is the ratio of the segments?

Back

The ratio of the segments is 10:20 or 1:2.

Front

What is the significance of parallel lines in the Side-Splitter Theorem?

Back

Parallel lines create proportional segments on the sides of the triangle.