Question

ex 2. given: gh || ij, ∠igj ≅ ∠hjg prove: ig ≅ hj

Explanation:

Step1: Identify the given information

We are given that \( GJ\parallel IH \), so \( \angle IGJ=\angle HJG \) (alternate - interior angles). Also, \( \angle IGJ\cong\angle HJG \) (given), and \( JG = JG \) (common side).

Step2: Apply the ASA (Angle - Side - Angle) congruence criterion

In \( \triangle IGJ \) and \( \triangle HJG \):

• \( \angle IGJ=\angle HJG \) (alternate - interior angles from \( GJ\parallel IH \))
• \( JG = JG \) (reflexive property)
• \( \angle IJG=\angle HGJ \) (alternate - interior angles from \( GJ\parallel IH \))

By the ASA congruence criterion, \( \triangle IGJ\cong\triangle HJG \).

Step3: Use the CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since \( \triangle IGJ\cong\triangle HJG \), then \( \overline{IG}\cong\overline{HJ} \) (CPCTC).

Answer:

\(\overline{IG}\cong\overline{HJ}\)