Side Splitter and Right Triangle Similarity Review

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

Define similar triangles.

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

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 do you find the length of a side in similar triangles?

Back

To find the length of a side in similar triangles, set up a proportion using the lengths of the corresponding sides.

Front

What is the formula for the area of similar triangles?

Back

If the ratio of the sides of two similar triangles is a:b, then the ratio of their areas is a²:b².

Front

Solve for x: If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, and AC = x, DF = 16, find x.

Back

x = 8.

Front

What is the significance of the right triangle in similarity?

Back

Right triangles are often used in similarity because they provide a clear relationship between angles and sides, making it easier to apply the properties of similar triangles.

Front

If two triangles have one angle equal and the sides including that angle proportional, what can be concluded?

Back

The two triangles are similar.

Front

Find the missing length: Triangle ABC is similar to triangle DEF. If AB = 6, DE = 9, and AC = 12, what is DF?

Back

DF = 18.