∠AEC is justified as a right angle through the definition of perpendicular bisectors; where point E divides both rods into equal parts forming four angles totaling 180 degrees when paired oppositely. Therefore, the correct answer is 'Definition of perpendicular bisector'.
In the given diagram, Kyle is working on creating a frame for a model car and has pieced two rods together. We are tasked with justifying why ∠AEC is a right angle. The most appropriate justification can be derived from the definition of perpendicular bisector.
In geometry, a perpendicular bisector is a line that divides another line into two equal parts at a 90-degree angle. In the context of the diagram provided, we observe that point E is where the two rods intersect, dividing each rod into two equal segments: AE and EB for one rod, and CE and ED for the other.
The intersection at point E forms four angles: ∠AEC, ∠BEC, ∠CED, and ∠AED. Given that each pair of opposite angles are equal in measure due to the properties of perpendicular bisectors (each angle being supplementary to its adjacent angle), it can be inferred that these pairs of opposite angles sum up to 180 degrees.
Since AE is opposite to EC and both are straight lines intersecting at E, it implies that they form linear pairs with their adjacent lines; hence each pair sums up to 180 degrees. This further implies that each angle in these pairs must be 90 degrees to satisfy this condition.
Therefore, by applying the definition of perpendicular bisectors - which states that it divides another line into two equal parts at a 90-degree angle - we can confidently assert that ∠AEC is indeed a right angle as it satisfies all conditions outlined in this definition.