Similarity

Two triangles have their corresponding angles equal. What can we say about these triangles?

In △ABC and △DEF, if AB/DE = BC/EF = AC/DF, then the triangles are:

If two triangles are similar, then the ratio of their areas is equal to:

In △PQR and △XYZ, ∠P = ∠X, ∠Q = ∠Y and PQ = 5 cm, QR = 7 cm, XY = 10 cm. Find the length of YZ if the triangles are similar.

Two triangles have sides in the ratio 3:4:5 and 6:8:10 respectively. What can be said about these triangles?

In △ABC, DE is drawn parallel to BC such that AD = 3 cm, DB = 6 cm, AE = 4 cm. Find the length of EC.

In two similar triangles, the ratio of their perimeters is 5:7. If the area of the smaller triangle is 50 cm², find the area of the larger triangle.

In △ABC, a line DE is drawn parallel to BC such that it divides AB and AC in the ratio 2:3. Find the ratio of the areas of △ADE and trapezium DECB.

In △ABC, AB = 8 cm, AC = 6 cm, and BC = 10 cm. A triangle △DEF is similar to △ABC with scale factor 3/4. Find the length of side EF.

Two triangles are similar. The sides of the first triangle are 9 cm, 12 cm, and 15 cm. The perimeter of the second triangle is 72 cm. Find the length of the longest side of the second triangle.