similar triangles solving (overlap)

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 length of a side in similar triangles?

Back

Use the proportion of corresponding sides. If triangle A is similar to triangle B, then A1/A2 = B1/B2, where A1 and A2 are sides of triangle A, and B1 and B2 are sides of triangle B.

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 9, what is the ratio of their sides?

Back

The ratio of their sides is 6:9 or 2:3.

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 4:5, what can be said about their angles?

Back

The angles of the triangles are equal, and the triangles are similar.

Front

What is the purpose of using similar triangles in real-life applications?

Back

Similar triangles can be used to find distances that are difficult to measure directly, such as the height of a tree or a building.

Front

If triangle XYZ is similar to triangle PQR, and XY = 10, PQ = 15, what is the length of YZ if PR = 12?

Back

YZ = (10/15) * 12 = 8.

Front

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

Back

The ratio of their areas is equal to the square of the ratio of their corresponding sides.

Front

If the sides of two similar triangles are in the ratio 1:4, what is the ratio of their areas?

Back

The ratio of their areas is 1:16.