Similar Triangles

Front

What are similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

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 Side-Side-Side (SSS) similarity criterion?

Back

The SSS similarity criterion states that if the lengths of 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 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

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

Back

The ratio of their corresponding sides is 1:2.

Front

How do you find the height of an object using similar triangles?

Back

To find the height of an object using similar triangles, set up a proportion using the heights and distances of two similar triangles formed by the object and a reference triangle.

Front

If two triangles are similar, how do you find a missing side length?

Back

To find a missing side length in similar triangles, set up a proportion between the lengths of corresponding sides and solve for the unknown.

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 side lengths.

Front

If triangle XYZ is similar to triangle PQR and the length of side XY is 5 cm and side PQ is 10 cm, what is the scale factor?

Back

The scale factor is 2.

Front

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

Back

If two triangles have two pairs of corresponding angles that are equal, then the triangles are similar.