Similar Triangles

Front

What are similar triangles?

Back

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 AA criterion for triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar (AA ~).

Front

What is the SSS criterion for triangle similarity?

Back

If the lengths of the corresponding sides of two triangles are in proportion, the triangles are similar (SSS ~).

Front

What is the SAS criterion for triangle similarity?

Back

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 (SAS ~).

Front

How can you find the height of a tall object using similar triangles?

Back

By using a mirror or a shadow, you can create a proportion based on the height of the object and the distance from the observer.

Front

If triangle ABC is similar to triangle DEF, and AB = 6 cm, DE = 9 cm, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides. (6:9)² = 4:9.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles have sides in the ratio 3:4, what can be said about their similarity?

Back

If the corresponding angles are also equal, then the triangles are similar.

Front

How do you determine if two triangles are not similar?

Back

If the corresponding angles are not equal or the sides are not in proportion, the triangles are not similar.

Front

What is the significance of the mirror method in measuring heights?

Back

It utilizes the properties of similar triangles to find the height of an object indirectly.