Answer:
∆QRS / ∆XZY = 1/2
Explanation:
You want the similarity ratio of ∆QRS to ∆XZY. Side lengths are marked in the diagram.
The similarity ratio will be the ratio of two corresponding side lengths.
Corresponding sides
You can find corresponding sides several ways:
- Use the similarity statement to identify corresponding vertices. A side will be defined by 2 of them. Use vertex identifiers that are in the same positions in both triangle names: QR : XZ (first two vertices listed), for example.
- Use the markings in the figure to identify corresponding sides. Corresponding sides will have the same angle marks at either end. For example, the side marked 1 in ∆QRS has 1-arc and 3-arc angle markings at its ends. The side marked 2 in ∆XZY also has 1-arc and 3-arc angle markings at either end. It will be the corresponding side.
- Use side lengths. When both triangles have their side lengths sorted into increasing order, the corresponding numbers are corresponding sides. The side lengths in ∆QRS are {1, 2, 2}. In ∆XZY, they are {2, 4, 4}.
The ratios of corresponding sides are 1:2, 2:4, and 2:4. The 2:4 ratios reduce to 1:2, which is the answer you're looking for. Written as a fraction, the ratio is ...
1/2 . . . . ratio of ∆QRS to ∆XZY