Question

Write congruence statements comparing the corresponding parts in each set of congruent figures.

A. AB ≅ A'B', BC ≅ B'C', AC ≅ A'C'
B. AB ≅ A'C', BC ≅ B'C', AC ≅ A'B'
C. AB ≅ AC, BC ≅ B'C', AC ≅ A'B'
D. AB ≅ BC, BC ≅ A'C', AC ≅ B'C'

Answer 1

In comparing congruent figures, congruence statements must correctly match corresponding parts of each figure. For congruent triangles, sides and angles of one are congruent to the corresponding parts of the other. Additionally, understanding fundamental principles like the commutative property is critical when dealing with equations or expressions.

Step-by-step explanation:

When comparing congruent figures and their corresponding parts, it is essential to match each part of one figure with its equivalent part in the other figure. This applies to congruent triangles, where the sides and angles of one triangle are congruent to the corresponding sides and angles of another triangle.

For example, if triangles ABC and A'B'C' are congruent, a correct congruence statement would be AB ≅ A'B', BC ≅ B'C', and AC ≅ A'C', which aligns with option A. This states that side AB of triangle ABC is congruent to side A'B' of triangle A'B'C', just as sides BC and AC are congruent to their corresponding sides B'C' and A'C'. It is important to ensure that the order of the vertices in the congruence statement correctly matches the corresponding parts of each figure.

When dealing with equations or expressions, it's crucial to understand the principles underlying the problem. For instance, understanding that A + B = B + A expresses the commutative property of addition, which is true not only for geometric figures but also in arithmetic operations.