Question

complete the congruence statement.
ijgh ≅ \boxed{\quad}

Explanation:

Step1: Match the corresponding vertices

When two polygons are congruent, their corresponding vertices, angles, and sides are equal. For quadrilateral \(IJGH\), we need to find the congruent quadrilateral by matching the order of side - lengths and angles.

Step2: Determine the congruent quadrilateral

By observing the side - length and angle measures (assuming the other quadrilateral in the un - shown context has vertices in the order that matches the given side - lengths \(11\)mm, \(15\)mm, \(44\)mm, \(47\)mm and angles \(91^{\circ}\), \(138^{\circ}\), \(101^{\circ}\), \(30^{\circ}\) in order). The congruence statement is based on the correspondence of vertices. If we assume the other quadrilateral has vertices \(K\), \(L\), \(M\), \(N\) (in the correct order of matching sides and angles), we can use the property of congruent polygons.

Let's assume the other quadrilateral is \(KLMN\) (a general notation for the congruent quadrilateral). But if we follow the side - length and angle order:

• The side \(IJ = 47\)mm, \(JG=11\)mm, \(GH = 15\)mm, \(HI=44\)mm
• Angles \(\angle J=91^{\circ}\), \(\angle G = 138^{\circ}\), \(\angle H=101^{\circ}\), \(\angle I = 30^{\circ}\)

If we consider the standard congruence notation for polygons (matching vertices in order of side - length and angle measures), we can write the congruence statement.

Answer:

\(IJGH\cong KLMN\) (assuming the other quadrilateral has vertices \(K\), \(L\), \(M\), \(N\) in the order that matches the side - lengths and angles. If there is a specific named quadrilateral in the original problem - set (not shown here in full), replace \(KLMN\) with the correct name. For example, if the other quadrilateral is \(PQRS\) with \(PQ = 47\)mm, \(QR = 11\)mm, \(RS=15\)mm, \(SP = 44\)mm and angles \(\angle Q = 91^{\circ}\), \(\angle R=138^{\circ}\), \(\angle S = 101^{\circ}\), \(\angle P=30^{\circ}\), then \(IJGH\cong PQRS\))