Identify the Special Quadrilateral: Analyzing a Kite's Properties

Kite Properties with Visual Analysis

Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the quadrilateral a kite?
00:03 2 pairs of adjacent sides are equal
00:08 A quadrilateral with 2 pairs of equal adjacent sides is a kite
00:12 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:

AAABBBCCCDDD

2

Step-by-step solution

To determine the type of quadrilateral depicted, let us analyze its geometric properties.

  • Firstly, assess the side lengths: The shape appears to have two pairs of equal adjacent sides, which is a defining characteristic of a deltoid (kite).
  • Secondly, check the nature of angles: Every interior angle in the quadrilateral is less than 180 degrees, indicating that the shape is convex.
  • Finally, confirm the symmetrical quality: The symmetry of the shape suggests that it aligns with the properties of a convex deltoid, also known as a kite.

In conclusion, by confirming these properties, we identify the quadrilateral as a Convex deltoid.

Thus, the correct answer is: Convex deltoid.

3

Final Answer

Convex deltoid

Key Points to Remember

Essential concepts to master this topic
  • Definition: Kite has two pairs of equal adjacent sides
  • Technique: Check if all interior angles are less than 180° for convexity
  • Check: Verify diagonal symmetry and equal adjacent side pairs ✓

Common Mistakes

Avoid these frequent errors
  • Confusing concave vs convex kites
    Don't just look at the shape's overall appearance = wrong classification! A kite is concave only if one interior angle exceeds 180°, creating an inward dent. Always examine each interior angle individually to determine convexity.

Practice Quiz

Test your knowledge with interactive questions

Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

FAQ

Everything you need to know about this question

How can I tell if a quadrilateral is a kite?

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Look for two pairs of equal adjacent sides! In this figure, sides AB and AD appear equal, and sides CB and CD appear equal. This is the key defining property of a kite.

What's the difference between convex and concave kites?

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A convex kite has all interior angles less than 180°, making it 'bulge outward.' A concave kite has one interior angle greater than 180°, creating an inward dent or 'arrowhead' shape.

Why does the diagonal symmetry matter?

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Kites have one line of symmetry along their main diagonal! This diagonal connects the vertices where unequal sides meet and bisects the other diagonal at right angles.

Can a kite have all four sides equal?

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Yes! When all four sides are equal, the kite becomes a special case called a rhombus. So every rhombus is technically a kite, but not every kite is a rhombus.

How do I identify the vertices in a kite?

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Look for the vertex angle (where unequal sides meet) and the non-vertex angles (where equal sides meet). In this kite ABCD, A and C are vertex angles.

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