Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

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

Back

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

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

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 find the length of a side in similar triangles?

Back

Use the proportion of the corresponding sides. If triangle ABC is similar to triangle DEF, then AB/DE = AC/DF = BC/EF.

Front

If triangle ABC is similar to triangle DEF, and AB = 10, DE = 5, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides. (10/5)² = 4.

Front

In similar triangles, if one triangle has a height of 6 cm and the corresponding height in the other triangle is 3 cm, what is the ratio of their heights?

Back

The ratio of their heights is 6:3 or 2:1.

Front

If a pole 4 meters tall casts a shadow of 7 meters, and a tower casts a shadow of 133 meters, how do you find the height of the tower?

Back

Set up a proportion: 4/7 = height of tower/133. Solve for the height of the tower.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of AB is 14 and DE is 7, what is the scale factor?

Back

The scale factor is 14/7 = 2.