Similar Triangles

Front

What are similar triangles?

Back

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

Front

What does AA stand for in triangle similarity?

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 stand for in triangle similarity?

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 stand for in triangle similarity?

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

Are congruent triangles also similar?

Back

True. Congruent triangles are similar because they have the same shape and size.

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

No, they are not similar unless the corresponding angles are also equal.

Front

How do you determine if triangles are similar using proportions?

Back

You can set up a proportion comparing the lengths of corresponding sides. If the ratios are equal, the triangles are 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 similarity: AB/DE = AC/DF => 4/8 = 6/DF => DF = 12.)

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle XYZ is similar to triangle PQR, and angle X = 30°, what is angle P?

Back

Angle P = 30°. (Corresponding angles of similar triangles are equal.)