Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity are: 1) AA (Angle-Angle) - If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2) SAS (Side-Angle-Side) - If one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, the triangles are similar. 3) SSS (Side-Side-Side) - If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does AA criterion stand for?

Back

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

Front

What does SAS criterion stand for?

Back

SAS criterion stands for Side-Angle-Side criterion, which states that if one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

Front

What does SSS criterion stand for?

Back

SSS criterion stands for Side-Side-Side criterion, which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

If two triangles have two equal angles, what can we conclude about them?

Back

If two triangles have two equal angles, we can conclude that the triangles are similar by the AA criterion.

Front

Can two triangles be similar if they have no equal angles?

Back

No, two triangles cannot be similar if they have no equal angles. Similar triangles must have at least two equal angles.

Front

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

Back

Yes, triangle A and triangle B are similar because their corresponding sides are in proportion (3:6, 4:8, 5:10).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are in proportion.