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) criterion for similarity?

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 has sides a, b, c and triangle B has sides x, y, z, then a/x = b/y = c/z.

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) criterion for similarity?

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, making them similar.

Front

Solve for x: If triangle ABC is similar to triangle DEF, and AB = 8, DE = 12, and BC = x, EF = 18, find x.

Back

x = (8/12) * 18 = 12.

Front

What is the importance of the corresponding angles in similar triangles?

Back

Corresponding angles being equal ensures that the triangles maintain the same shape.

Front

If the lengths of two corresponding sides of similar triangles are 10 cm and 15 cm, what is the scale factor?

Back

The scale factor is 10:15 or 2:3.

Front

If triangle XYZ is similar to triangle PQR, and the length of XY is 5 cm and PQ is 10 cm, what is the ratio of their areas?

Back

The ratio of their areas is (5^2):(10^2) = 1:4.