Similarity of Triangles

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may have different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the Angle-Angle (AA) similarity criterion?

Back

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

Front

What is the Side-Side-Side (SSS) similarity criterion?

Back

The Side-Side-Side (SSS) similarity criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

The Side-Angle-Side (SAS) similarity criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

How do you write a proportion for similar triangles?

Back

To write a proportion for similar triangles, set the ratios of the lengths of corresponding sides equal to each other. For example, if triangle ABC is similar to triangle DEF, then AB/DE = AC/DF.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 3, what is the ratio of their sides?

Back

The ratio of their sides is 6:3, which simplifies to 2:1.

Front

Are two triangles with angles measuring 30°, 60°, and 90° similar to each other?

Back

Yes, two triangles with angles measuring 30°, 60°, and 90° are similar because they have the same angle measures.

Front

If triangle XYZ is similar to triangle PQR, and XY = 4 and PQ = 8, what is the value of the ratio XY:PQ?

Back

The value of the ratio XY:PQ is 4:8, which simplifies to 1:2.

Front

What does it mean if two triangles are not similar?

Back

If two triangles are not similar, it means that their corresponding angles are not equal, or their corresponding sides are not in proportion.

Front

How can you determine if two triangles are similar using their side lengths?

Back

To determine if two triangles are similar using their side lengths, check if the ratios of the lengths of corresponding sides are equal.