Question

A suspect of a crime is traveling on 26th Street toward Cherry Street. The diagram shows the locations of the suspect and a police officer. Your friend says that the officer should wait at point C to intercept the suspect because the officer will have the same distance to travel no matter which route the suspect takes. Is your friend correct? Explain.

Answer 1

Answer:

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Answer 2

Answer:

• yes, By the Angle Bisector Theorem. $AC=EC$
• yes; By the Perpendicular Bisector Theorem. $AC=EC$
• no. You cannot use the Angle Bisector Theorem to determine that $AC=EC$
• no. Point $C$ is not equidistant from 26th Street and Peach Street

Step-by-step explanation:

AC is not equal to CE based on the angle bisector theorem.

The answer is: C. NO, you cannot use the angle bisector theorem to determine that $AC = CE.$

Angle Bisector Theorem

When a line segment splits an angle of a triangle, it also divides the opposite side, but in such a way that the two segments are proportional to the other two sides of the triangle, according to the angle bisector theorem. However, the two portions are incompatible with one another.

• In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that $AC = CE.$

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