Question
What do you notice about quadrilaterals with the same side lengths?
The side lengths of all of the shapes below are shown in inches. Select all the quadrilaterals with side lengths of 6, 10, 12, and 18 inches.
18
6
10
12
6
10
12
18
18
10
12
8
18
6
12
10
Good work!
The purple and orange quadrilaterals are two of the quadrilaterals you just selected. They have the same side lengths. Are these quadrilaterals identical?
6
10
12
18
18
6
10
12
Yes
No
Nice!
Now let’s look at two of the other quadrilaterals with side lengths of 6, 10, 12, and 18 inches. Are these quadrilaterals identical?
6
10
12
18
18
6
12
10
Yes
No
Excellent!
What do you notice about these quadrilaterals with the same four side lengths?
6
10
12
18
18
6
10
12
18
6
12
10
There
that can be made with these four side lengths.
The side lengths of all of the shapes below are shown in inches. Select all the quadrilaterals with side lengths of 6, 10, 12, and 18 inches.
18
6
10
12
6
10
12
18
18
10
12
8
18
6
12
10
Good work!
The purple and orange quadrilaterals are two of the quadrilaterals you just selected. They have the same side lengths. Are these quadrilaterals identical?
6
10
12
18
18
6
10
12
Yes
No
Nice!
Now let’s look at two of the other quadrilaterals with side lengths of 6, 10, 12, and 18 inches. Are these quadrilaterals identical?
6
10
12
18
18
6
12
10
Yes
No
Excellent!
What do you notice about these quadrilaterals with the same four side lengths?
6
10
12
18
18
6
10
12
18
6
12
10
There
that can be made with these four side lengths.
Answers
GPT-4o mini
The quadrilaterals with the same side lengths of 6, 10, 12, and 18 inches can have different shapes and arrangements, meaning they are not necessarily identical even if they consist of the same side lengths. When quadrilaterals have the same four side lengths, they belong to a category of shapes known as "congruent" shapes. However, congruent means they have identical dimensions and shape, but they may not be the same quadrilateral due to variations in angles and the arrangement of sides.
In your examples, even though the quadrilaterals have the same side lengths, their configurations can be different, leading to distinct shapes that may not be congruent. This means that a quadrilateral can be formed in multiple ways, given the same set of side lengths, leading to different quadrilaterals.
In conclusion, the key takeaways are:
1. **Different Arrangements**: Quadrilaterals with the same side lengths can have different shapes and arrangements.
2. **Non-Congruent**: Such quadrilaterals may not be identical or congruent even though their side lengths match.
3. **Multiple Shapes**: There can be multiple quadrilaterals that can be made with the same four side lengths.
In your specific example, this indicates that there may be multiple unique quadrilaterals that conform to the specified side lengths. Thus, when discussing the difference or sameness of the shapes, the focus should be on their geometric properties, including angle measurements and overall shape formation, beyond just their side lengths.
In your examples, even though the quadrilaterals have the same side lengths, their configurations can be different, leading to distinct shapes that may not be congruent. This means that a quadrilateral can be formed in multiple ways, given the same set of side lengths, leading to different quadrilaterals.
In conclusion, the key takeaways are:
1. **Different Arrangements**: Quadrilaterals with the same side lengths can have different shapes and arrangements.
2. **Non-Congruent**: Such quadrilaterals may not be identical or congruent even though their side lengths match.
3. **Multiple Shapes**: There can be multiple quadrilaterals that can be made with the same four side lengths.
In your specific example, this indicates that there may be multiple unique quadrilaterals that conform to the specified side lengths. Thus, when discussing the difference or sameness of the shapes, the focus should be on their geometric properties, including angle measurements and overall shape formation, beyond just their side lengths.