Quadrilateral Identification: Analyzing a Four-Sided Figure with Marked Angles

Q: How can I tell if a quadrilateral is a deltoid just by looking?

Look for two pairs of adjacent sides that appear equal in length. A deltoid often has a kite-like shape with one axis of symmetry running through two opposite vertices.

Q: What's the difference between concave and convex deltoids?

A convex deltoid has all interior angles less than 180°, so it 'bulges outward.' A concave deltoid has at least one interior angle greater than 180°, creating an 'inward dent' or arrow shape.

Q: Do the equal sides have to be next to each other?

Yes! In a deltoid, the equal sides must be adjacent (touching at a vertex). If opposite sides are equal instead, you have a parallelogram, not a deltoid.

Q: Is every kite a deltoid?

Yes! 'Kite' and 'deltoid' are different names for the same quadrilateral. Both describe a four-sided figure with two pairs of adjacent equal sides.

Q: How do I know this deltoid isn't concave?

Look at the shape - it doesn't have any 'dents' or inward angles. All vertices point outward, and the symmetry confirms all interior angles are less than 180°, making it convex.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What square is this?

00:03 Pairs of equal sides

00:08 Therefore the square 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:

2

Step-by-step solution

Initially, let us examine the basic properties of a deltoid (or kite):

A quadrilateral is classified as a deltoid if:

It has two distinct pairs of adjacent sides that are equal in length.

In the question's image, we observe the following:

There are lines connecting A to B, B to C, C to D, and D to A, suggesting a typical quadrilateral.
The shape, given its central symmetry (as it is formed by joining these particular points which extend equal lines), is reminiscent of a symmetric or bilaterally mirrored formation.
Given the symmetry, it suggests all internal angles are less than 180 degrees, confirming the figure as a convex shape.

From this analysis, the quadrilateral satisfies the characteristic of having pairs of equal adjacent sides which confirms it as a deltoid. The symmetry suggests it is not concave (which occurs when at least one interior angle is greater than 180 degrees).

Therefore, the given quadrilateral, based on its properties and symmetry, is a convex deltoid.

3

Final Answer

Convex deltoid

Key Points to Remember

Essential concepts to master this topic

Deltoid Definition: Two pairs of adjacent sides must be equal in length
Convexity Test: All interior angles less than 180° means convex shape
Verification: Check symmetry and angle markings confirm equal adjacent sides ✓

Common Mistakes

Avoid these frequent errors

Confusing deltoid with rhombus properties
Don't assume all four sides are equal like in a rhombus = wrong classification! A deltoid only needs two pairs of adjacent equal sides, not all four equal. Always identify the specific pairs of equal adjacent sides to confirm deltoid properties.

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

How can I tell if a quadrilateral is a deltoid just by looking?

+

Look for two pairs of adjacent sides that appear equal in length. A deltoid often has a kite-like shape with one axis of symmetry running through two opposite vertices.

What's the difference between concave and convex deltoids?

+

A convex deltoid has all interior angles less than 180°, so it 'bulges outward.' A concave deltoid has at least one interior angle greater than 180°, creating an 'inward dent' or arrow shape.

Do the equal sides have to be next to each other?

+

Yes! In a deltoid, the equal sides must be adjacent (touching at a vertex). If opposite sides are equal instead, you have a parallelogram, not a deltoid.

Can I use the angle marks to identify the deltoid?

+

The angle marks in the diagram help confirm the shape's properties, but focus on side lengths for deltoid classification. Equal angles don't guarantee equal sides.

Is every kite a deltoid?

+

Yes! 'Kite' and 'deltoid' are different names for the same quadrilateral. Both describe a four-sided figure with two pairs of adjacent equal sides.

How do I know this deltoid isn't concave?

+

Look at the shape - it doesn't have any 'dents' or inward angles. All vertices point outward, and the symmetry confirms all interior angles are less than 180°, making it convex.

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Quadrilateral Identification: Analyzing a Four-Sided Figure with Marked Angles

Deltoid Classification with Convexity Analysis

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