Solving 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

How do you find the missing length in similar triangles?

Back

Use the proportion of the lengths of corresponding sides. If triangle A has sides a1, a2, a3 and triangle B has sides b1, b2, b3, then a1/b1 = a2/b2 = a3/b3.

Front

If triangle ABC is similar to triangle DEF, and AB = 10, DE = 5, what is the ratio of their areas?

Back

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Here, (10/5)² = 4.

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

If two triangles have sides in the ratio 3:4, what is the ratio of their perimeters?

Back

The ratio of their perimeters is also 3:4.

Front

What is the relationship between the corresponding angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle XYZ is similar to triangle PQR, and XY = 6, PQ = 3, what is the length of YZ if PR = 4?

Back

Using the proportion, YZ/4 = 6/3, so YZ = 8.

Front

What is the importance of the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of similar triangles, which helps in finding missing lengths.

Front

If the lengths of two similar triangles are in the ratio 1:2, what is the ratio of their areas?

Back

The ratio of their areas is 1:4, since (1:2)² = 1:4.