Question

figure a is translated 3 units right and 2 units up. the translated figure is labeled figure b. figure b is reflected over the x-axis. the reflected figure is labeled figure c. which best explains why figure a is congruent to figure c? a ≅ b and b ≅ c each triangle is a right triangle. each triangle is an isosceles triangle. a ≅ a, b ≅ b, c ≅ c

Explanation:

Step1: Understand congruent triangles

Congruent triangles have the same shape and size. Transformations like translation (sliding) and reflection (flipping) do not change the size and shape of a figure.

Step2: Analyze the transformations

Figure A is translated (moved) to get Figure B, and Figure B is reflected (flipped) to get Figure C. Since translation and reflection are rigid transformations (they preserve the size and shape of the figure), \(A\cong B\) and \(B\cong C\). By the transitive property of congruence (\(if\ a = b\ and\ b = c,\ then\ a = c\)), \(A\cong C\)

Answer:

A. \(A\cong B\) and \(B\cong C\)