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 congruence

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

Step2: Analyze the options

• Option "Each triangle is a right triangle": This only tells about the type of triangle (right - angled) but doesn't explain congruence. Congruence is about shape and size equality, not just angle type.
• Option "Each triangle is an isosceles triangle": Similar to the above, this tells about the side - angle property (two sides equal in an isosceles triangle) but not about congruence.
• Option "A≅A, B≅B, C≅C": This is a trivial statement (a figure is congruent to itself) and doesn't explain the congruence relationship between A, B, and C.
• Option "A≅B and B≅C": Since translation and reflection are rigid transformations (they preserve shape and size), figure A (after translation) becomes congruent to figure B, and figure B (after reflection) becomes congruent to figure C. By the transitive property of congruence (if \(A\cong B\) and \(B\cong C\), then \(A\cong C\)), this option explains why figure A is congruent to figure C.

Answer:

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