Question
Line CD intersects with segment AB at E so that the measure of AE equals the measure of EB and angle CEB is a right angle.
Kyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why ∠AEC is a right angle.
A. Definition of parallel lines
B. Definition of perpendicular bisector
C. Definition of complementary angles
D. Definition of adjacent angles
Answers
GPT-4o mini
In the given problem, you have line CD intersecting segment AB at point E, where AE = EB and angle CEB is a right angle.
From this situation, we can conclude that segment AB has been bisected at point E, and since angle CEB is a right angle, it indicates that line CD is perpendicular to segment AB at point E.
To justify why angle AEC is a right angle, we can consider the definitions involved:
The most appropriate choice from the options given is:
**B. Definition of perpendicular bisector**
A perpendicular bisector is a line that cuts another line segment into two equal parts at a right angle. Since AE = EB (indicating that line CD bisects AB) and CEB is a right angle, it follows that angle AEC must also be a right angle because points A, E, and C form a right triangle with the right angle at E, confirming the definition of angle properties in a right triangle setup.
Thus the correct answer is **B. Definition of perpendicular bisector**.
From this situation, we can conclude that segment AB has been bisected at point E, and since angle CEB is a right angle, it indicates that line CD is perpendicular to segment AB at point E.
To justify why angle AEC is a right angle, we can consider the definitions involved:
The most appropriate choice from the options given is:
**B. Definition of perpendicular bisector**
A perpendicular bisector is a line that cuts another line segment into two equal parts at a right angle. Since AE = EB (indicating that line CD bisects AB) and CEB is a right angle, it follows that angle AEC must also be a right angle because points A, E, and C form a right triangle with the right angle at E, confirming the definition of angle properties in a right triangle setup.
Thus the correct answer is **B. Definition of perpendicular bisector**.