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 does AA similarity criterion stand for?

Back

AA stands for Angle-Angle. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS similarity criterion stand for?

Back

SSS stands for Side-Side-Side. If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS similarity criterion stand for?

Back

SAS stands for Side-Angle-Side. If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

How can you determine if two triangles are not similar?

Back

If none of the similarity criteria (AA, SSS, SAS) are satisfied, the triangles are not similar.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12 (Using the ratio of sides: AB/DE = AC/DF => 4/8 = 6/DF => DF = 12).

Front

If two triangles have one angle of 60 degrees and the other angles are 30 degrees and 90 degrees respectively, are they similar?

Back

Yes, they are similar by AA criterion (60° = 60° and 30° + 90° = 120° which is the third angle).

Front

What is the relationship between the sides of similar triangles?

Back

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

Front

If triangle XYZ is similar to triangle PQR, and the ratio of their sides is 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 4:9 (the square of the ratio of their sides).

Front

If two triangles are similar and the length of one side of the first triangle is 10 cm, what is the length of the corresponding side in the second triangle if the ratio of similarity is 1:4?

Back

The length of the corresponding side in the second triangle is 40 cm (10 cm * 4).