Question

hk bisects ∠ihj and hi ≅ hj. complete the proof that δhjk ≅ δhik.

(image of triangle with vertices i, h, j and k on ij)

	statement	reason
1	hk bisects ∠ihj	given
2	hi ≅ hj	given
3	∠ihk ≅ ∠jhk
4	hk ≅ hk
5	δhjk ≅ δhik	sas

Explanation:

Step1: Analyze Statement 3

Since \( \overleftrightarrow{HK} \) bisects \( \angle IHJ \), by the definition of an angle bisector, it divides \( \angle IHJ \) into two congruent angles. So \( \angle IHK \cong \angle JHK \) because an angle bisector creates two equal angles.

Step2: Analyze Statement 4

The segment \( \overline{HK} \) is common to both \( \triangle HJK \) and \( \triangle HIK \). By the Reflexive Property of Congruence, any segment is congruent to itself. So \( \overline{HK} \cong \overline{HK} \) by the Reflexive Property.

Answer:

For Statement 3: Reason is "Definition of Angle Bisector"
For Statement 4: Reason is "Reflexive Property of Congruence"