Question

practice problems the second h - shaped polygon is a scaled copy of the first.
a. show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. consider using colored pencils to highlight corresponding parts or labeling some of the vertices.

Explanation:

Step1: Identify Corresponding Points

Let's label the top - left vertex of the large H - shaped polygon as point \(A\) and the top - left vertex of the small (scaled) H - shaped polygon as point \(A'\). These two points are corresponding because the small polygon is a scaled copy of the large one, and the top - left vertices are in the same relative position within their respective H - shapes.

Step2: Identify Corresponding Sides (First Pair)

Look at the vertical side on the left - most part of the large H - shape. Let's say this side has a length (in terms of grid units) of \(l_1\). The vertical side on the left - most part of the small H - shape is a corresponding side. If the large side spans, for example, 4 grid squares vertically, the small side will span a number of grid squares that is related by the scale factor. Let's call the large left - vertical side \(S_1\) and the small left - vertical side \(S_1'\).

Step3: Identify Corresponding Sides (Second Pair)

Now, consider the horizontal middle bar of the large H - shape. Let's call this side \(S_2\). The horizontal middle bar of the small H - shape is a corresponding side, \(S_2'\). The length of \(S_2\) and \(S_2'\) are related by the same scale factor as the other corresponding sides because the small polygon is a scaled copy.

(Note: Since this is a visual - based problem with a grid, the actual identification can be done by looking at the relative positions. For example, if we take the large H - shape, the top - left corner (let's say at grid coordinate \((x_1,y_1)\)) and the top - left corner of the small H - shape (at grid coordinate \((x_2,y_2)\)) where the transformation from \((x_1,y_1)\) to \((x_2,y_2)\) is a scaling (and possibly translation) that preserves the shape. For the sides, the left - most vertical segment of the large H and the left - most vertical segment of the small H are corresponding, and the middle horizontal segment of the large H and the middle horizontal segment of the small H are corresponding.)

Answer:

• Corresponding points: Let the top - left vertex of the large H - polygon be \(A\) and the top - left vertex of the small H - polygon be \(A'\).
• Corresponding sides:
• The left - most vertical side of the large H - polygon and the left - most vertical side of the small H - polygon.
• The middle horizontal side of the large H - polygon and the middle horizontal side of the small H - polygon.

(To show this, you can label the vertices of the large H as \(A, B, C, \cdots\) and the vertices of the small H as \(A', B', C', \cdots\) such that \(A\) corresponds to \(A'\), \(B\) corresponds to \(B'\), etc., and then identify the sides between corresponding vertices.)