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 determine if two triangles are similar using angle measures?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar by the AA criterion.

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B has sides of lengths 6, 8, and 10, are the triangles similar?

Back

Yes, triangle A and triangle B are similar by the SSS criterion because the sides are in proportion (3:6, 4:8, 5:10).

Front

What does it mean if two triangles are not similar?

Back

It means that the triangles do not have the same shape; their corresponding angles are not equal, and/or their corresponding sides are not in proportion.

Front

If triangle A has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of a similar triangle will also be 30°, 60°, and 90°.

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional.

Front

Can two triangles with one angle equal and two sides equal be similar?

Back

Yes, they can be similar by the SAS criterion if the included angle is equal.