Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but not necessarily the same 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) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2) SSS (Side-Side-Side) Criterion: If the sides of two triangles are in proportion, the triangles are similar. 3) SAS (Side-Angle-Side) Criterion: 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

What does the AA criterion state?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Front

What does the SSS criterion state?

Back

The SSS criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the two triangles are similar.

Front

What does the SAS criterion state?

Back

The SAS criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angle is equal, then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 6 (since the triangles are similar, the sides are in proportion: AB/DE = AC/DF => 4/8 = 6/DF => DF = 6).

Front

If two triangles have one angle of 60 degrees and the other two angles are unknown, can we determine if they are similar?

Back

No, we cannot determine if they are similar without knowing the measures of the other two angles.

Front

If triangle XYZ is similar to triangle PQR, and XY = 5, XZ = 10, and PQ = 15, what is the length of QR?

Back

QR = 30 (since XY/XZ = PQ/QR => 5/10 = 15/QR => QR = 30).

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.