Question

△ghk ≅ △ihj. complete the proof that ∠gjk ≅ ∠ikj.

image of a geometric figure with points j, i, h, g, k

statement	reason
2. \\(\overline{gk} ≅ \overline{ij}\\)	cpctc
3. \\(\overline{gh} ≅ \overline{hj}\\)	cpctc
4. \\(\overline{hk} ≅ \overline{hj}\\)	cpctc
5. gj = gh + hj	additive property of length
6. ik = hi + hk	additive property of length
7. gj = hi + hk	blank for reason
8. gj = ik	transitive property of equality
9. \\(\overline{jk} ≅ \overline{jk}\\)	reflexive property of congruence
10. △gjk ≅ △ikj	sss
11. ∠gjk ≅ ∠ikj	cpctc

Explanation:

Step1: Analyze Step 5 and Step 3

From Step 3, we know \( \overline{GH} \cong \overline{HJ} \), so \( GH = HJ \)? Wait, no, Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, original Step 3: \( \overline{GH} \cong \overline{HJ} \)? Wait, no, the given Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, no, looking back: Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, no, the problem's Step 5: \( GJ = GH + HJ \) (wait, maybe typo? Wait, original Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? 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Answer:

Step1: Analyze Step 5 and Step 3

From Step 3, we know \( \overline{GH} \cong \overline{HJ} \), so \( GH = HJ \)? Wait, no, Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, original Step 3: \( \overline{GH} \cong \overline{HJ} \)? Wait, no, the given Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, no, looking back: Step 3 is \( \overline{GH} \cong \overline{HJ} \)? Wait, no, the problem's Step 5: \( GJ = GH + HJ \) (wait, maybe typo? Wait, original Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? Wait, no, the user's Step 5: \( GJ = GH + HJ \)? 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