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 does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity, which states that if the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side similarity, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

How do you find the scale factor between two similar triangles?

Back

The scale factor is found by dividing the length of a side of one triangle by the corresponding side of the other triangle.

Front

If Triangle ABC is similar to Triangle DEF, and AB = 10 cm, DE = 15 cm, what is the scale factor?

Back

The scale factor is 10:15 or simplified to 2:3.

Front

What is the relationship between the areas of two 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

If the scale factor of two similar triangles is 3:4, what is the ratio of their areas?

Back

The ratio of their areas is 3²:4², which is 9:16.

Front

How can you determine if two triangles are not similar?

Back

Two triangles are not similar if their corresponding angles are not equal or their corresponding sides are not in proportion.

Front

What is the significance of corresponding sides in similar triangles?

Back

Corresponding sides in similar triangles maintain the same ratio, which is crucial for establishing similarity.