M7|L6 Building Polygons (Part 1)Sign out

Check to see if the quadrilaterals with the same side lengths are identical or not.
The side lengths of all of the shapes below are shown in inches. Select all the quadrilaterals with side lengths of 4, 5, 8, and 9 inches.

4
8
5
9

9
8
5
4

4
8
6
9

8
4
5
9
Great job!
The purple and orange quadrilaterals are two of the quadrilaterals you just selected. They have the same side lengths. Are these quadrilaterals identical?
8
4
5
9
9
8
5
4

Yes

No

1 answer

To determine if two quadrilaterals with the same side lengths are identical, we must examine not just the lengths of the sides but also the arrangement of those sides.

In the case of the quadrilaterals you mentioned:

One quadrilateral has side lengths \( 8, 4, 5, 9 \).
The other quadrilateral has side lengths \( 9, 8, 5, 4 \).

Since both quadrilaterals have the same side lengths but arranged differently, they may or may not be identical. Quadrilaterals are considered identical if one can be transformed into the other through rotations or reflections without changing the side length sequence.

Typically, as long as the sequence of the lengths is consistent (whether clockwise or counterclockwise), the quadrilaterals can be identified as the same.

In this case:

The two sets of side lengths can be reordered to reflect a consistent sequence.
Therefore, these two quadrilaterals are identical.

So, your answer would be Yes, the quadrilaterals are identical.