**Problem 2** Select **all** of the pairs of polygons in which the image appears to be the result of a dilation of the pre-image. (*Select all that apply.*) **Description of Each Diagram:** 1. **Top Left Diagram:** - Shows two polygons with a series of dotted lines connecting corresponding vertices. The inner polygon appears smaller and is located inside the larger polygon. However, the shapes appear different, suggesting a transformation other than dilation. 2. **Top Right Diagram:** - Displays two polygons connected by dashed lines extending from a common external point (center of dilation). The smaller polygon is inside the larger one and maintains a similar shape, indicative of dilation. 3. **Bottom Left Diagram:** - Features two polygons in which a smaller polygon is nested within a larger one. Both polygons share a similar shape and are connected by lines drawn from each vertex of the inner polygon extending towards corresponding points on the outer polygon, suggesting dilation. 4. **Bottom Right Diagram:** - Two polygons are connected by dashed lines emanating from a point outside both polygons. The polygons have a different orientation and do not appear to maintain similarity in shape, indicating a transformation other than dilation. **Instructions for Solution:** Carefully analyze each pair of polygons to identify those that maintain proportionality and similarity indicating a dilation transformation. Select those that fulfill these criteria.

Use the Pythagorean Theorem to find the missing side for the right-angled triangle given in the figure below. It has base 112 m and height 15 m. If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -). 15 n 112 n • If you need to use the square root symbol, as in x = V17, type it using: sqrt(17) • Units need to be entered using their standard abbreviations, without a period. For example, type m for meters, m^2 for square meters, etc.

Elementary school students were given a geometry assignment they were to measure the area of several rectangles to measure the diagonal of the rectangle as shown on the table.

Could you explain in detail or steps how to do these type of special triangles?