Mr. Garlin Similar Triangles Theorems

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What does AA stand for in triangle similarity?

Back

AA stands for 'Angle-Angle'. It is a criterion for triangle similarity that states if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for 'Side-Angle-Side'. It is a criterion for triangle similarity that states 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 SSS stand for in triangle similarity?

Back

SSS stands for 'Side-Side-Side'. It is a criterion for triangle similarity that states if the lengths of all three sides of one triangle are proportional to the lengths of the corresponding sides of another triangle, then the triangles are similar.

Front

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

Back

To determine if two triangles are similar using the AA criterion, check if two angles of one triangle are equal to two angles of the other triangle. If they are, the triangles are similar.

Front

Back

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. This means that the ratio of the lengths of one pair of corresponding sides is equal to the ratio of the lengths of another pair of corresponding sides.

Front

What does it mean if two triangles are 'Not Similar'?

Back

If two triangles are 'Not Similar', it means that they do not have the same shape. This could be due to differences in angle measures or side lengths that do not maintain proportionality.

Front

Provide an example of using the SSS criterion to prove triangle similarity.

Back

If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF has sides of lengths 6, 8, and 10, then by the SSS criterion, triangle ABC is similar to triangle DEF because the ratios of the corresponding sides are equal (3:6 = 1:2, 4:8 = 1:2, 5:10 = 1:2).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal. This means that if triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.