State whether ABC and AED are congruent. Justify your answer.
To determine whether ABC and AED are congruent, we need to compare their corresponding sides and angles.
Looking at the sides:
- Side AB corresponds to side AE.
- Side BC corresponds to side ED.
- Side AC corresponds to side AD.
Since the corresponding sides are equal, AB = AE, BC = ED, and AC = AD, we can say that the sides of ABC and AED are congruent.
Looking at the angles:
- Angle ABC corresponds to angle AED.
- Angle BCA corresponds to angle EDA.
- Angle CAB corresponds to angle EAD.
Since the corresponding angles are equal, angle ABC = angle AED, angle BCA = angle EDA, and angle CAB = angle EAD, we can say that the angles of ABC and AED are congruent.
Based on the information above, we can conclude that ABC and AED are congruent.