Triangle Similarity Postulates

Front

What is the definition of similar triangles?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does the AA Similarity Postulate state?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does the SSS Similarity Postulate state?

Back

If the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does the SAS Similarity Postulate state?

Back

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

Write a similarity statement for triangles ΔABC and ΔDEF if ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.

Back

ΔABC ∼ ΔDEF.

Front

If ΔXYZ ∼ ΔPQR, and XY = 4 cm, YZ = 6 cm, and PQ = 8 cm, what is the length of QR?

Back

QR = 12 cm (using the proportionality of sides in similar triangles).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles have sides in the ratio 3:5, are they similar?

Back

Yes, if the corresponding angles are also equal.

Front

How can you determine if two triangles are not similar?

Back

If the corresponding angles are not equal or the sides are not in proportion, the triangles are not similar.

Front

What is an example of using the AA Similarity Postulate?

Back

If ∠A = ∠D and ∠B = ∠E, then ΔABC ∼ ΔDEF by AA Similarity.