Quadrilateral Classification: Identify the Geometric Shape ABCD

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

A deltoid and kite are the same shape! Both terms describe a quadrilateral with two pairs of equal adjacent sides. The word 'kite' is more common in elementary math.

Q: How do I tell if sides are adjacent or opposite?

Adjacent sides share a common vertex (corner). For example, in quadrilateral ABCD, sides AB and BC are adjacent because they both connect to point B. Opposite sides don't touch each other.

Q: Can a deltoid be concave?

Yes! A concave deltoid has one interior angle greater than $180^{\circ}$, creating an 'arrow' or 'dart' shape. A convex deltoid has all angles less than $180^{\circ}$.

Q: What if none of the adjacent sides are equal?

Then it's not a deltoid! The defining property of a deltoid is having exactly two pairs of equal adjacent sides. Without this property, classify it as a general quadrilateral.

Q: How can I measure sides from a diagram?

Look for tick marks indicating equal lengthsUse coordinate points to calculate distancesCheck if the diagram provides measurementsSometimes you need to assume based on visual appearance

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the quadrilateral a kite?

00:03 We don't know anything about any sides

00:10 Therefore we cannot know if it's a kite or not

00:14 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, let's analyze the given quadrilateral ABCD by examining its geometric properties:

Step 1: Identifying characteristics of a deltoid
A deltoid, or kite, is a quadrilateral that has two distinct pairs of adjacent sides that are equal. To classify a shape as a deltoid, we need to verify these properties.
Step 2: Examining the quadrilateral ABCD
The deltoid can be either concave or convex. If the shape is concave, it will have an indentation, meaning at least one angle is greater than $180^{\circ}$ . A convex deltoid does not have such an indentation.
Step 3: Analyze the sides of ABCD
Looking at the segments from the given points:
- Verify if pairs of adjacent sides are equal.
If we cannot find two equal pairs of adjacent sides, the quadrilateral is not a deltoid.
Step 4: Drawing conclusions
Having analyzed the sides of the quadrilateral, if none of the pairs of adjacent sides conform to the deltoid property as outlined—two pairs of equal adjacent sides—then ABCD is identified as not a deltoid.

Therefore, the correct answer is: Not deltoid.

3

Final Answer

Not deltoid

Key Points to Remember

Essential concepts to master this topic

Deltoid Rule: Must have two pairs of equal adjacent sides
Technique: Check if AB = AD and BC = CD for deltoid properties
Check: Verify adjacent side pairs are equal, not opposite sides ✓

Common Mistakes

Avoid these frequent errors

Confusing deltoids with rhombus properties
Don't assume all four sides must be equal = wrong classification! A deltoid only needs two pairs of equal adjacent sides, not all sides equal. Always identify which specific sides are adjacent and check if pairs match.

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?

+

A deltoid and kite are the same shape! Both terms describe a quadrilateral with two pairs of equal adjacent sides. The word 'kite' is more common in elementary math.

How do I tell if sides are adjacent or opposite?

+

Adjacent sides share a common vertex (corner). For example, in quadrilateral ABCD, sides AB and BC are adjacent because they both connect to point B. Opposite sides don't touch each other.

Can a deltoid be concave?

+

Yes! A concave deltoid has one interior angle greater than $180^{\circ}$ , creating an 'arrow' or 'dart' shape. A convex deltoid has all angles less than $180^{\circ}$ .

What if none of the adjacent sides are equal?

+

Then it's not a deltoid! The defining property of a deltoid is having exactly two pairs of equal adjacent sides. Without this property, classify it as a general quadrilateral.

How can I measure sides from a diagram?

+

Look for tick marks indicating equal lengths
Use coordinate points to calculate distances
Check if the diagram provides measurements
Sometimes you need to assume based on visual appearance

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Quadrilateral Classification: Identify the Geometric Shape ABCD

Deltoid Classification with Adjacent Side Properties

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