Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity is a concept in geometry where two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are proportional.

Front

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

Back

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

Front

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

Back

The 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 relationship between corresponding sides of similar triangles?

Back

The corresponding sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

If the height of a tree is 20 m, what is the height of a similar tree if the ratio of similarity is 1:3?

Back

The height of the similar tree is 60 m.

Front

What is the meaning of 'corresponding angles' in similar triangles?

Back

Corresponding angles are angles in two triangles that are in the same relative position. If two triangles are similar, their corresponding angles are equal.

Front

If triangle GHI is similar to triangle JKL, and GH = 5 cm, what is the length of JK if the ratio of similarity is 2:5?

Back

JK = 12.5 cm.

Front

What is the importance of triangle similarity in real-life applications?

Back

Triangle similarity is used in various fields such as architecture, engineering, and art to create proportional designs and to solve problems involving indirect measurements.