Quadrilateral Classification: Identifying a Kite-Shaped Figure

Indicate the correct answer

The next quadrilateral is:

To solve this problem, let's examine the properties of the given quadrilateral:

• Step 1: Identify if the quadrilateral has any interior angles greater than $180^\circ$.
• Step 2: Verify if the quadrilateral has two pairs of contiguous equal-length sides, which would qualify it as a deltoid (kite).
• Step 3: Determine whether the shape is concave or convex based on the angles and diagonal layout.

Analysis: In the provided diagram, the quadrilateral has a vertex that forms an interconnecting internal angle greater than $180^\circ$, showing that it's a concave shape. The sides $AB = BC$ and $CD = DA$ suggest two pairs of contiguous equal sides.

Based on the properties identified:

• One angle exceeds $180^\circ$, indicating a concave form.
• It has two sets of adjacent sides that are equal, confirming it as a deltoid.

Therefore, the shape shown in the illustration matches the properties of a concave deltoid.

The correct answer is thus Concave deltoid.