Identify the Special Quadrilateral: Analysis of ABCD with Right Angles

Q: What's the difference between a deltoid and a kite?

They're the same shape! A deltoid is just another name for a kite. Both have two pairs of adjacent equal sides and one line of symmetry.

Q: How can I tell if a deltoid is convex or concave?

Look at all the interior angles. If every angle is less than 180°, it's convex. If any angle is greater than 180°, it's concave.

Q: Do all deltoids have right angles?

No! The right angle markers in this diagram just show perpendicular diagonals. Most deltoids don't have right angles at their vertices - that would make them a special square kite.

Q: What makes this shape NOT a regular quadrilateral?

A deltoid has two pairs of equal adjacent sides, not four equal sides like a square or rhombus. This unequal side pattern creates its distinctive kite shape.

Q: Can I identify a deltoid by looking at its diagonals?

Yes! In a deltoid, the diagonals are perpendicular (meet at 90°) and one diagonal bisects the other. You can see this clearly in the diagram with the right angle markers.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Indicate the correct answer

The next quadrilateral is:

2

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.

3

Final Answer

Convex deltoid

Key Points to Remember

Essential concepts to master this topic

Definition: Deltoid has two pairs of adjacent equal sides
Technique: Check interior angles - all < 180° means convex
Check: Verify shape symmetry and angle measurements match kite properties ✓

Common Mistakes

Avoid these frequent errors

Confusing deltoid with rhombus
Don't assume all four sides are equal = wrong classification! A deltoid has only two pairs of adjacent equal sides, not four equal sides like a rhombus. Always identify the specific side relationships first.

Practice Quiz

Test your knowledge with interactive questions

Indicate the correct answer

The next quadrilateral is:

FAQ

Everything you need to know about this question

What's the difference between a deltoid and a kite?

+

They're the same shape! A deltoid is just another name for a kite. Both have two pairs of adjacent equal sides and one line of symmetry.

How can I tell if a deltoid is convex or concave?

+

Look at all the interior angles. If every angle is less than 180°, it's convex. If any angle is greater than 180°, it's concave.

Do all deltoids have right angles?

+

No! The right angle markers in this diagram just show perpendicular diagonals. Most deltoids don't have right angles at their vertices - that would make them a special square kite.

What makes this shape NOT a regular quadrilateral?

+

A deltoid has two pairs of equal adjacent sides, not four equal sides like a square or rhombus. This unequal side pattern creates its distinctive kite shape.

Can I identify a deltoid by looking at its diagonals?

+

Yes! In a deltoid, the diagonals are perpendicular (meet at 90°) and one diagonal bisects the other. You can see this clearly in the diagram with the right angle markers.

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Identify the Special Quadrilateral: Analysis of ABCD with Right Angles

Kite Identification with Convexity Analysis

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