Question

hk bisects ∠ihj. complete the proof that (overline{jk}congoverline{ik}).

1 (hk) bisects (angle ihj) given
2 (overline{hj}congoverline{hi})
3 (angle ihkcongangle jhk)
4 (overline{hk}congoverline{hk})
5 (\triangle hikcong\triangle hjk) sas
6 (overline{jk}congoverline{ik}) cpctc

Explanation:

Step1: Identify the reason for $\overline{HJ}\cong\overline{HI}$

From the diagram, we can see that $\overline{HJ}$ and $\overline{HI}$ are marked as equal. So the reason is "Given (marked in the diagram)".

Step2: Identify the reason for $\angle IHK\cong\angle JHK$

Since $\overleftrightarrow{HK}$ bisects $\angle IHJ$, by the definition of an angle - bisector, it divides $\angle IHJ$ into two equal angles. So the reason is "Definition of angle bisector".

Step3: Identify the reason for $\overline{HK}\cong\overline{HK}$

A segment is congruent to itself. This is the reflexive property of congruence. So the reason is "Reflexive property of congruence".

Answer:

1. Given (marked in the diagram)
2. Definition of angle bisector
3. Reflexive property of congruence