Question

1. (5pts) diego made the shape on the left, and elena made the shape on the right. each shape uses 5 circles.

select all the true statements.
a. the smallest circle in diegos design is congruent to the smallest circle in elenas design.
b. diegos design is congruent to elenas design.
c. elenas design is a translation of diegos design.
d. the largest circle in elenas design is congruent to the largest circle in diegos design.
e. each circle in elenas design has a congruent circle within diegos design.

Explanation:

Step1: Analyze congruent circles

Congruent circles have the same radius. Looking at the smallest circles in both designs, they appear to have the same size (radius), so statement A is true.

Step2: Analyze the entire designs

The overall shapes of Diego's and Elena's designs are different. Diego's is a set of concentric circles centered in a more "circular - like" overall shape, while Elena's has a more "asymmetric" (in terms of the overall outline formed by the circles) shape. So Diego's design is not congruent to Elena's design (statement B is false), and Elena's design is not a translation of Diego's design (translation would just move the shape without changing its orientation or relative positions in a non - uniform way, but here the internal structure relative to the overall shape is different, so statement C is false).

Step3: Analyze the largest circles

The largest circles in both designs have the same radius (by visual inspection of the grid - based drawing), so statement D is true.

Step4: Analyze each circle comparison

Since the smallest and largest circles are congruent (from steps 1 and 3), and assuming the intermediate - sized circles (by the nature of the grid - based construction where the growth pattern for radius can be assumed similar in terms of step - by - step increase) have the same radii in pairs (one from Diego's and one from Elena's design), statement E is true.

Answer:

A. The smallest circle in Diego’s design is congruent to the smallest circle in Elena’s design.
D. The largest circle in Elena’s design is congruent to the largest circle in Diego’s design.
E. Each circle in Elena’s design has a congruent circle within Diego’s design.