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 equal to the ratio of the lengths 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. For example, if x is the length of one segment, and the other segments are known, set up the proportion as x/a = b/c.

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 based on the lengths of the segments.

Front

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

Back

x = 5.

Front

What does it mean for triangles to be similar in the context of the Side-Splitter Theorem?

Back

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

Front

If a triangle has a side length of 12 and is divided by a line parallel to the base, what can you conclude about the segments?

Back

The segments created on the other two sides will be proportional to the lengths of the sides of the triangle.

Front

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

Back

It helps in finding unknown lengths in triangles and understanding the properties of similar triangles.

Front

If a triangle has sides of lengths 6 and 9, and a line divides the triangle, what is the proportion of the segments?

Back

The proportion of the segments will be 6:9 or 2:3.

Front

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

Back

Check if the ratios of the corresponding sides are equal.