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

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

Back

If a line divides two sides of a triangle, you can set up the proportion as: (length of segment on one side) / (length of corresponding segment on the other side) = (length of segment on the other side) / (length of corresponding segment on the first side).

Front

If a line divides two sides of a triangle into segments of lengths 7 and x, and the corresponding segments are 14 and 15, what is the proportion?

Back

x / 15 = 7 / 14.

Front

What is the value of x if 7 / x = 15 / 14?

Back

x = 6.

Front

If a triangle has sides divided into segments of lengths 21 and x, and the corresponding segments are 18 and 24, what is the value of x?

Back

x = 21.

Front

What is the missing length if the segments are 4 and x, and the corresponding segments are 10 and 12?

Back

x = 10.

Front

What is the first step in applying the Side-Splitter Theorem?

Back

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

Front

What does it mean for segments to be proportional?

Back

Segments are proportional if the ratios of their lengths are equal.

Front

If two triangles are similar, how does the Side-Splitter Theorem apply?

Back

The Side-Splitter Theorem can be used to find missing lengths in similar triangles by setting up proportions based on corresponding sides.

Front

What is an example of a real-world application of the Side-Splitter Theorem?

Back

Determining the height of a tree using similar triangles formed by a shadow and a measuring stick.