Identify the Special Quadrilateral: Analysis of ABCD with Right Angles

Video Solution

Solution Steps

00:00 Is the quadrilateral a kite?

00:03 A pair of adjacent sides are equal

00:06 The main diagonal bisects the secondary diagonal

00:16 The diagonals are perpendicular to each other

00:23 Therefore triangle BCD is isosceles

00:29 A quadrilateral with 2 pairs of equal adjacent sides is a kite

00:32 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to identify whether the depicted quadrilateral is a convex deltoid, a concave deltoid, or not a deltoid.

Step 1: Identify key features of a deltoid:
A deltoid, or kite, has two distinct pairs of adjacent equal sides. A convex deltoid will have all interior angles less than 180°, while a concave deltoid has at least one angle greater than 180°.
Step 2: Examine the quadrilateral's properties:
Visually assess the shape to determine if it fits the deltoid definitions. Here, the quadrilateral seems to match the structure of a kite, as there are two pairs of adjacent sides that appear equal. Furthermore, all the interior angles seem to be less than 180°, indicating that it is a convex shape.
Step 3: Final determination:
Given that the quadrilateral appears to meet the criteria of a convex deltoid with no angles exceeding 180°, we can conclude that the correct answer for the quadrilateral is "Convex deltoid."

Therefore, the depicted quadrilateral is a Convex deltoid.