Proportions in Triangles

Front

What is a proportion in the context of triangles?

Back

A proportion in triangles refers to the equality of two ratios, often used to compare the lengths of corresponding sides of similar triangles.

Front

What is the Triangle Proportionality Theorem?

Back

The Triangle Proportionality 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 solve for a variable in a proportion?

Back

To solve for a variable in a proportion, cross-multiply the ratios and then isolate the variable.

Front

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

Back

If two triangles are similar, the lengths of their corresponding sides are in proportion.

Front

What is the formula for finding the length of a side in similar triangles?

Back

The formula is: (length of side in triangle 1) / (length of corresponding side in triangle 2) = (length of another side in triangle 1) / (length of corresponding side in triangle 2).

Front

What is the significance of the AA criterion for triangle similarity?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

How can you determine if two triangles are similar using side lengths?

Back

Two triangles are similar if the ratios of their corresponding side lengths are equal.

Front

What is the relationship between the areas of similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

What is the concept of scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

Front

How do you apply the concept of proportions to solve real-world problems involving triangles?

Back

You can set up a proportion based on the relationships between the sides of the triangles and solve for unknown lengths.