Question

1. diego made the design on the left, and elena made the design on the right. each design 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: Recall congruence definition

Two geometric figures are congruent if they have the same size and shape.

Step2: Analyze statement a

The smallest circles in both designs appear to have the same radius, so they are congruent. This statement is true.

Step3: Analyze statement b

Diego's and Elena's designs have different overall shapes due to the arrangement of circles, so they are not congruent. This statement is false.

Step4: Analyze statement c

A translation is a rigid - motion that moves a figure without changing its shape, size, or orientation. Elena's design has a different orientation and shape compared to Diego's, so it is not a translation. This statement is false.

Step5: Analyze statement d

The largest circles in both designs seem to have the same radius, so they are congruent. This statement is true.

Step6: Analyze statement e

The circles in Elena's design are arranged differently in terms of vertical and horizontal positions compared to Diego's, and not all circles have corresponding congruent circles in the other design. This statement is false.

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.