7.4 Side Splitter Theorem

Front

What does the Side Splitter Theorem state?

Back

If a line is parallel to one side of a triangle and intersects the other two sides, then the ratios of the lengths of the segments created on those sides are equal.

Front

In the context of the Side Splitter Theorem, if a line divides two sides of a triangle into segments of lengths AB and BC, what is the relationship expressed by the theorem?

Back

The relationship is expressed as \( \frac{AB}{BC} = \frac{AE}{ED} \) where AE and ED are segments on the third side.

Front

What is the definition of similar figures?

Back

Two figures are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The lengths of their corresponding sides are proportional.

Front

How can you find the missing length in a triangle using the Side Splitter Theorem?

Back

You can set up a proportion based on the lengths of the segments created by the parallel line and solve for the missing length.

Front

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

Back

Parallel lines create proportional segments on the intersected sides of the triangle, which is the basis for the theorem.

Front

If a triangle has sides of lengths 10 and 15, and a line parallel to one side creates segments of lengths 4 and x on the other two sides, how do you find x?

Back

Set up the proportion \( \frac{10}{15} = \frac{4}{x} \) and solve for x.

Front

What is the formula for finding the ratio of the lengths of two sides of a triangle when a line is drawn parallel to one side?

Back

The formula is \( \frac{AB}{BC} = \frac{AE}{ED} \), where AB and BC are segments on one side and AE and ED are segments on the other.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How do you determine if two triangles are similar using the Side Splitter Theorem?

Back

If the sides of the triangles are in proportion and the corresponding angles are equal, then the triangles are similar.