Triangle Similarity Theorems

Front

What is Triangle Similarity?

Back

Triangle similarity means that two triangles 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 stand for?

Back

AA Similarity stands for 'Angle-Angle Similarity'. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS Similarity stand for?

Back

SSS Similarity stands for 'Side-Side-Side Similarity'. If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS Similarity stand for?

Back

SAS Similarity stands for 'Side-Angle-Side Similarity'. 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.

Front

State the Triangle Angle Bisector Theorem.

Back

The Triangle Angle Bisector Theorem states that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the other two sides.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If the sides of triangle ABC are 3, 4, and 5, and triangle DEF is similar to triangle ABC with a scale factor of 2, what are the lengths of the sides of triangle DEF?

Back

The sides of triangle DEF will be 6, 8, and 10.

Front

How do 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.

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional to each other.

Front

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

Back

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