Question

1. which is the definition of congruent? a) if two figures have the same shape, then they are congruent. b) if two figures have the same area, then they are congruent. c) if there is a sequence of rotations, reflections, and translations that take one figure to another, then they are congruent. d) if there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent. 3. consider the two triangles in the following diagram. there is a sequence of rigid - transformations that takes a to a, b to b, and c to c. the same sequence takes d to d. draw and label d.

Explanation:

Step1: Recall congruence definition

Two figures are congruent if there is a sequence of rotations, reflections, and translations that take one figure to the other. This is the key concept for answering the multiple - choice part and for finding the location of \(D'\).

Step2: For the multiple - choice

The correct definition of congruent figures is that if there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent. So the answer to the multiple - choice is C.

Step3: For finding \(D'\)

Since there is a sequence of rigid transformations that takes \(A\) to \(A'\), \(B\) to \(B'\), and \(C\) to \(C'\), the relative position of \(D\) with respect to \(A\), \(B\), and \(C\) must be the same as the relative position of \(D'\) with respect to \(A'\), \(B'\), and \(C'\). Measure the distances and angles of \(D\) from \(A\), \(B\), \(C\) in \(\triangle ABC\) and replicate them in \(\triangle A'B'C'\) to find and label \(D'\).

Answer:

For the multiple - choice: C. If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.
For drawing \(D'\): Use the relative position of \(D\) in \(\triangle ABC\) to find and label \(D'\) in \(\triangle A'B'C'\) based on the same rigid - transformation sequence.