September 26th Flashcardziz Triangle Similarity Postulates

Front

What does SSS similarity postulate state?

Back

If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

Front

What does SAS similarity postulate state?

Back

If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does AA similarity postulate state?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

How can you determine if two triangles are similar using SSS?

Back

Check if the ratios of the lengths of corresponding sides are equal.

Front

How can you determine if two triangles are similar using SAS?

Back

Check if two sides are in proportion and the angle between them is equal.

Front

How can you determine if two triangles are similar using AA?

Back

Check if two angles in one triangle are equal to two angles in another triangle.

Front

What is the significance of triangle similarity in geometry?

Back

Similar triangles have the same shape but not necessarily the same size, allowing for the use of proportional reasoning.

Front

Provide an example of SSS similarity. Triangle ABC has sides 3, 4, 5 and triangle DEF has sides 6, 8, 10. Are they similar?

Back

Yes, they are similar by SSS because the sides are in proportion (3:6 = 1:2, 4:8 = 1:2, 5:10 = 1:2).

Front

Provide an example of SAS similarity. Triangle GHI has sides 5, 12 and an included angle of 60 degrees, and triangle JKL has sides 10, 24 and an included angle of 60 degrees. Are they similar?

Back

Yes, they are similar by SAS because the sides are in proportion (5:10 = 1:2, 12:24 = 1:2) and the included angle is equal.

Front

Provide an example of AA similarity. Triangle MNO has angles 30 degrees and 60 degrees, and triangle PQR has angles 30 degrees and 60 degrees. Are they similar?

Back

Yes, they are similar by AA because two angles are equal.