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

1 answer

To determine which quadrilaterals have identical side lengths, we need to compare the sets of side lengths for each shape listed.

Here are the side lengths given:

Quadrilateral 1: 4, 8, 5, 9
Quadrilateral 2: 9, 8, 5, 4
Quadrilateral 3: 4, 8, 6, 9
Quadrilateral 4: 8, 4, 5, 9

Now, let's sort and compare the side lengths of each quadrilateral:

Quadrilateral 1: (4, 5, 8, 9) → sorted: 4, 5, 8, 9
Quadrilateral 2: (9, 8, 5, 4) → sorted: 4, 5, 8, 9
Quadrilateral 3: (4, 8, 6, 9) → sorted: 4, 6, 8, 9
Quadrilateral 4: (8, 4, 5, 9) → sorted: 4, 5, 8, 9

From this comparison, we can observe:

Quadrilaterals 1, 2, and 4 all have identical side lengths (4, 5, 8, 9).
Quadrilateral 3 has different side lengths (4, 6, 8, 9) and does not match.

Thus, the quadrilaterals with the same side lengths are:

Quadrilateral 1
Quadrilateral 2
Quadrilateral 4