Define similar triangles and state two conditions for similarity. Also find the length of side PR in the provided similar triangles.

Let the smaller triangle have base $B_1 = 8.2 \text{ cm}$ and height $H_1 = 6.1 \text{ cm}$.
Let the larger triangle have base $B_2 = 12.3 \text{ cm}$ and height $H_2 = PR$.
Since the triangles are similar, the ratio of corresponding sides is equal:

22. In two similar triangles, the ratio of corresponding sides is 2:3. If one side of the smaller triangle is 10cm, find the corresponding side of the larger triangle.

Let $S_s$ be the side of the smaller triangle and $S_l$ be the corresponding side of the larger triangle.
The ratio of corresponding sides (smaller to larger) is $\frac{S_s}{S_l} = \frac{2}{3}$.

Given $S_s = 10 \text{ cm}$.

23. Below are similar triangles with ratio of corresponding sides 3:2. If length XY = 8, find DF.

Let the first triangle be XYZ and the second triangle be DEF.
From the image, triangle XYZ appears smaller than triangle DEF.
The ratio of corresponding sides is given as 3:2. To match the visual representation where DF is larger than XY, we assume the ratio is (side of larger triangle) : (side of smaller triangle) = 3:2.
So, $\frac{DF}{XY} = \frac{3}{2}$.

Given $XY = 8$.