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

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

If two triangles are similar, how do you find the length of a side in one triangle if you know the length of the corresponding side in the other triangle?

Back

Use the proportion of the lengths of the corresponding sides to set up a ratio and solve for the unknown length.

Front

If triangle XYZ is similar to triangle PQR, and XY = 6 cm, YZ = 9 cm, and PQ = 12 cm, what is the length of QR?

Back

QR = (YZ / XY) * PQ = (9 / 6) * 12 = 18 cm.

Front

What does it mean if two triangles are not similar?

Back

It means that their corresponding angles are not equal, or their corresponding sides are not in proportion.

Front

Back

Front

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

Back

If all three angles of one triangle are equal to the three angles of another triangle, then the triangles are similar.