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 the lengths of their corresponding sides are proportional.

Front

What are the criteria for triangle similarity?

Back

The three main 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) SAS (Side-Angle-Side) Criterion: If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, the triangles are similar. 3) SSS (Side-Side-Side) Criterion: If the sides of one triangle are in proportion to the sides of another triangle, the triangles are similar.

Front

What does the AA criterion state?

Back

The AA (Angle-Angle) 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 SAS criterion state?

Back

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

Front

What does the SSS criterion state?

Back

The SSS (Side-Side-Side) criterion states that if the lengths of the sides of one triangle are proportional to the lengths of the sides of another triangle, then the two triangles are similar.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

If triangle ABC is similar to triangle DEF, what can be said about the ratios of their corresponding sides?

Back

If triangle ABC is similar to triangle DEF, then the ratios of their corresponding sides are equal, i.e., \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \).

Front

How do you find the scale factor of similar triangles?

Back

The scale factor of similar triangles can be found by taking the ratio of the lengths of any two corresponding sides. For example, if triangle ABC is similar to triangle DEF, the scale factor can be calculated as \( \frac{AB}{DE} \).

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. If the scale factor is \( k \), then the ratio of the areas is \( k^2 \).

Front

If triangle ABC is similar to triangle DEF with a scale factor of 2:3, what is the ratio of their areas?

Back

If the scale factor is 2:3, then the ratio of their areas is \( \left(\frac{2}{3}\right)^2 = \frac{4}{9} \).