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 AB and DE are 4 cm and 8 cm respectively, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides. Thus, (4/8)^2 = 1/4.

Front

How do you find the length of a side in similar triangles?

Back

Use the proportion of the corresponding sides. If triangle ABC is similar to triangle DEF, then \( \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} \).

Front

If two triangles have sides of lengths 6 cm, 8 cm, and 10 cm, and 3 cm, 4 cm, and 5 cm respectively, are they similar?

Back

Yes, they are similar because the sides are in proportion (6:3 = 2:1, 8:4 = 2:1, 10:5 = 2:1).

Front

What is the relationship between the heights of two similar triangles?

Back

The heights of two similar triangles are in the same ratio as their corresponding sides.

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 (10 cm / 5 cm).

Front

How do you solve for a missing side in similar triangles?

Back

Set up a proportion using the lengths of the corresponding sides and solve for the unknown.