Identify the type of quadrilateral shown in image 4 and explain why, based on the markings.

Image 4 Analysis:

The image shows a quadrilateral ABCD.

Observations from markings:

• Side AB is parallel to side DC (indicated by single arrows on both sides).
• Side AD is parallel to side BC (indicated by double arrows on both sides).
• Diagonal BD is drawn.
• Angles formed by the diagonal BD with sides AB and DC are marked as equal (single arc on ∠ABD and ∠BDC).
• Angles formed by the diagonal BD with sides AD and BC are marked as equal (double arc on ∠ADB and ∠DBC).

Conclusion:

Based on the markings:

• The opposite sides are parallel (AB || DC and AD || BC). This indicates that the quadrilateral is a parallelogram.
• The diagonal BD divides the parallelogram into two congruent triangles (∡ABD ≅ ∡CDB and ∡ADB ≅ ∡CBD). This is consistent with properties of a parallelogram where the diagonal creates congruent alternate interior angles.

  Therefore, the quadrilateral ABCD is a parallelogram.

Answer: The quadrilateral shown in image 4 is a parallelogram because both pairs of opposite sides are marked as parallel.