Question

△ghj is equilateral, j is the midpoint of (overline{ik}), and (overline{gk}congoverline{hi}). complete the proof that (angle kcongangle i).
statement
1 △ghj is equilateral
2 j is the midpoint of (overline{ik})
3 (overline{gk}congoverline{hi})
4 (overline{jk}congoverline{ji})
5
reason
given
given
given
definition of midpoint

Explanation:

Step1: Use the property of equilateral triangle

Since \(\triangle GHJ\) is equilateral, \(GH = GJ\) (All sides of an equilateral triangle are equal).

Step2: Prove \(\triangle GJK\cong\triangle HIJ\)

We have \(GK = HI\) (Given), \(JK = JI\) (Definition of mid - point), and \(GJ=GH\) (From step 1). By the Side - Side - Side (SSS) congruence criterion, \(\triangle GJK\cong\triangle HIJ\).

Step3: Use the property of congruent triangles

If \(\triangle GJK\cong\triangle HIJ\), then \(\angle K\cong\angle I\) (Corresponding parts of congruent triangles are congruent).

Answer:

\(\angle K\cong\angle I\)