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

What is a similarity statement?

Back

A similarity statement expresses that two triangles are similar, typically written as ΔABC~ΔDEF.

Front

If ΔABC~ΔDEF, what can be inferred about their angles?

Back

The corresponding angles of triangles ABC and DEF are equal.

Front

If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

Back

Yes, by SSS postulate, since the sides are in proportion (3:6, 4:8, 5:10).

Front

What is the ratio of the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.

Front

If two triangles are similar and the length of one side of the first triangle is 5 cm and the corresponding side of the second triangle is 10 cm, what is the scale factor?

Back

The scale factor is 2:1.