Corallary to 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

State the Corollary to the Side Splitter Theorem.

Back

The Corollary to the Side Splitter Theorem states that if two triangles are similar, then the lengths of corresponding sides are proportional.

Front

If a triangle has sides of lengths 8, 10, and x, and a parallel line divides the triangle into two smaller triangles, what is the value of x if the other side is 6?

Back

x = 6. (Using the proportionality of sides in similar triangles.)

Front

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

Back

Set up a proportion using the lengths of the sides that are divided by the parallel line and solve for the missing length.

Front

If a triangle has sides of lengths 12 and 16, and a parallel line divides one side into lengths of 4 and x, what is the value of x?

Back

x = 5. (Using the proportion 4/12 = x/16.)

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are in proportion.

Front

If two triangles are similar and one has a side length of 10, what is the corresponding side length in the other triangle if the ratio of similarity is 2:3?

Back

The corresponding side length is 15. (10 * (3/2) = 15.)

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal or if the lengths of their corresponding sides are proportional.

Front

If a triangle has a base of 20 and a height of 10, what is the area of the triangle?

Back

Area = 1/2 * base * height = 100.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.