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 DE is parallel to BC in triangle ABC, and AD/DB = DE/BC, what does this imply?

Back

This implies that the lengths of segments AD and DB are proportional to the lengths of segments DE and BC.

Front

In triangle ABC, if AD = 3 and DB = 2, what is the ratio AD:DB?

Back

The ratio AD:DB is 3:2.

Front

If DE = 6 and BC = 10, what is the ratio DE:BC?

Back

The ratio DE:BC is 6:10 or simplified to 3:5.

Front

How do you find the length of a side using the Side-Splitter Theorem?

Back

To find the length of a side, set up a proportion using the lengths of the segments created by the parallel line.

Front

If AD = 3, DB = 2, and DE = 6, how do you find BC?

Back

Set up the proportion: AD/DB = DE/BC, which gives 3/2 = 6/BC. Cross-multiply to find BC = 10.

Front

What is the significance of parallel lines in triangles?

Back

Parallel lines in triangles create similar triangles, allowing for the use of proportional relationships.

Front

If CB = 3, CA = 10, and CE = 6 in triangle ACT, how do you find ET?

Back

Use the Side-Splitter Theorem: CB/CA = CE/ET, leading to 3/10 = 6/ET. Cross-multiply to find ET = 14.

Front

What is a practical application of the Side-Splitter Theorem?

Back

The Side-Splitter Theorem can be used in real-life situations such as architecture and engineering to determine lengths and proportions.

Front

If a triangle has sides of lengths 6, 8, and 10, and a line parallel to one side divides the other two sides, what can be inferred?

Back

The segments created by the parallel line will maintain the same ratio as the original sides of the triangle.