Question

finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons!
given: ( jkcong lk ). km bisects ( angle jkl )
prove: ( angle kjmcongangle klm )

Explanation:

Step1: First statement reason

The first statement \( JK\cong LK \) is given in the problem. So the reason for statement 1 is "Given".

Step2: Second statement

Since \( KM \) bisects \( \angle JKL \), by the definition of bisect, \( \angle JKM\cong\angle LKM \). So statement 2 is \( \angle JKM\cong\angle LKM \) and the reason is "Definition of Bisect".

Step3: Third statement

\( MK = MK \) (reflexive property). But since the reflexive property is already used for a reason (maybe in the given table structure, assume we are building the proof step - by - step). The third statement can be \( \triangle JKM\) and \( \triangle LKM\) have two sides and the included angle. We know \( JK = LK\) (from step 1), \( \angle JKM=\angle LKM\) (from step 2) and \( KM = KM\) (reflexive property). The reason for using these to prove triangles congruent is "SAS" (Side - Angle - Side) for statement 4 (assuming the order of filling).

Step4: Fifth statement reason

If \( \triangle JKM\cong\triangle LKM\) (by SAS), then by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \( \angle KJM\cong\angle KLM\). So the reason for statement 5 (\( \triangle JKM\cong\triangle LKM\)) is "SAS" and for statement 6 (\( \angle KJM\cong\angle KLM\)) is "CPCTC".

Answer:

1. Reason: Given
2. Statement: \( \angle JKM\cong\angle LKM\), Reason: Definition of Bisect
3. Statement: \( KM = KM\), Reason: Reflexive Property (already in the table, but if we consider the proof flow, we can assume the order of filling. If we follow the standard two - column proof for triangle congruence)
4. (Assuming the SAS step for triangle congruence)
5. Reason: SAS
6. Reason: CPCTC