Question

Here is an unlabeled polygon, along with its scaled copies Polygons A, B, C, and D. Select all of the statements that are true.

a) Polygon D is a scaled copy of Polygon A.
b) Polygon B is smaller than Polygon C.
c) Polygon A is congruent to Polygon C.
d) Polygon D is the largest among all.

Answer 1

The student's question involves comparing polygons to determine relationships such as scaling, congruence, and relative sizes. Key considerations include the shapes, side lengths, angles, and areas of the polygons involved.

Step-by-step explanation:

The question presented is related to polygons and involves understanding their properties, such as size, congruence, and scaling. When comparing polygons and identifying scaled copies, congruent figures, and their relative sizes, it is essential to consider the lengths of corresponding sides, angles, and overall shape.

• Polygon D is a scaled copy of Polygon A only if it has the same shape with proportional sides.
• Polygon B is smaller than Polygon C if its corresponding sides are shorter than those of Polygon C.
• Polygon A is congruent to Polygon C only if all corresponding sides and angles are equal, which means they are the same shape and size.
• Polygon D is the largest among all if its area is greater than the areas of Polygons A, B, and C.

When comparing the areas of different figures, like A1, A2, and A3, the comparison involves evaluating the size of each area to determine which one is greater, equal, or less. These concepts are fundamental in geometry, specifically when dealing with polygons and their attributes in a mathematical context.