Similar Triangles Postulates

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 does AA similarity mean?

Back

AA similarity (Angle-Angle) states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SSS similarity mean?

Back

SSS similarity (Side-Side-Side) states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does SAS similarity mean?

Back

SAS similarity (Side-Angle-Side) states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How can 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

Example of AA similarity: Triangle ABC and Triangle DEF have angles A = D and B = E. Are they similar?

Back

Yes, Triangle ABC is similar to Triangle DEF by AA similarity.

Front

Example of SSS similarity: Triangle GHI has sides 3, 4, 5 and Triangle JKL has sides 6, 8, 10. Are they similar?

Back

Yes, Triangle GHI is similar to Triangle JKL by SSS similarity (sides are in proportion 1:2).

Front

Example of SAS similarity: Triangle MNO has sides 5, 12 and an included angle of 60 degrees. Triangle PQR has sides 10, 24 and an included angle of 60 degrees. Are they similar?

Back

Yes, Triangle MNO is similar to Triangle PQR by SAS similarity.

Front

What is the significance of the similarity postulates?

Back

They provide criteria to determine whether two triangles are similar, which is essential in solving geometric problems.

Front

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

Back

The ratio of their areas is the square of the ratio of their corresponding sides.