AKS 4 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 apply the Side-Splitter Theorem to find missing lengths in a triangle?

Back

To apply the Side-Splitter Theorem, set up a proportion using the lengths of the segments created by the parallel line and solve for the missing length.

Front

If a triangle has sides of lengths 4, 6, and a segment created by a parallel line is 3, how do you find the missing length?

Back

Set up the proportion: 4/6 = 3/x, then cross-multiply and solve for x.

Front

What is the relationship between the segments created by a parallel line in a triangle?

Back

The segments are proportional to the lengths of the sides of the triangle that they are parallel to.

Front

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

Back

The corresponding sides of similar triangles are in proportion.

Front

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

Back

If a line divides two sides of a triangle proportionally, then it is parallel to the third side, indicating that the triangles are similar.

Front

What is the formula for finding the length of a segment using the Side-Splitter Theorem?

Back

If a line divides two sides of a triangle into segments of lengths a and b, and c and d, then a/b = c/d.

Front

In a triangle, if one side is 10 and the corresponding side in a similar triangle is 15, what is the ratio of similarity?

Back

The ratio of similarity is 10:15 or 2:3.

Front

What is the significance of the Side-Splitter Theorem in real-world applications?

Back

The Side-Splitter Theorem can be used in various fields such as architecture, engineering, and design to ensure proportionality and similarity in structures.

Front

How do you find the value of x in a proportion?

Back

Cross-multiply the terms in the proportion and solve for x.