Similarity Proofs

Front

What does SSS similarity mean?

Back

SSS similarity means that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does AA similarity mean?

Back

AA similarity means that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS similarity mean?

Back

SAS similarity means that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the definition of similarity ratio?

Back

The similarity ratio is the ratio of the lengths of corresponding sides of two similar figures.

Front

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

If the similarity ratio of two triangles is 2/3, what does this imply about their corresponding sides?

Back

It implies that the lengths of the corresponding sides of the triangles are in the ratio of 2:3.

Front

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

Back

You can determine if two triangles are similar using the AA postulate by showing that two angles of one triangle are equal to two angles of another triangle.

Front

What is the significance of the SAS similarity theorem?

Back

The SAS similarity theorem is significant because it allows us to prove the similarity of triangles when we know the lengths of two sides and the measure of the included angle.

Front

What is the formula for finding the scale factor (SF) between two similar triangles?

Back

The scale factor (SF) is found by dividing the length of a side of one triangle by the length of the corresponding side of the other triangle.

Front

If triangle XYZ has sides of lengths 4, 6, and 8, and triangle PQR has sides of lengths 2, 3, and 4, are the triangles similar?

Back

Yes, triangle XYZ and triangle PQR are similar by SSS similarity because the sides are in proportion (4:2, 6:3, 8:4).