Question

Which statement best explains whether ∆ABC is congruent to ∆DEF?

a. They have equal angles
b. They have equal side lengths
c. They have equal perimeters
d. They have equal areas

Answer 1

To determine if ∆ABC is congruent to ∆DEF, we must verify that they have equal angles and sides, as equal areas or perimeters do not ensure congruence.

Step-by-step explanation:

The statement that best explains whether ∆ABC is congruent to ∆DEF is that they have equal angles and equal side lengths. For two triangles to be congruent, they must satisfy the criteria of one of the congruence postulates (such as SSS, SAS, ASA, AAS, or HL), which means they have identical shapes and dimensions, but they may be flipped or rotated differently. However, having equal areas or equal perimeters does not necessarily mean the triangles are congruent.

Two triangles are congruent if all corresponding angles are equal. This means that the measures of all the angles in ∆ABC must be equal to the measures of all the angles in ∆DEF. If this condition is satisfied, the triangles are congruent.

For example, if angle A in ∆ABC is equal to angle D in ∆DEF, angle B is equal to angle E, and angle C is equal to angle F, then the triangles are congruent.