Do the following vertices form a parallelogram? Prove using the theorem that allows you to know that IF opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram.

To check if the vertices M(−4,3), E(2,5), L(6,2), T(0,0) form a parallelogram, we will calculate the lengths of the opposite sides: ME, EL, LT, and MT.

We will use the distance formula for points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Step 1: Calculate lengths of the sides

**Length of ME:**
\[
M(-4, 3) \quad E(2, 5)
\]
\[
ME = \sqrt{(2 - (-4))^2 + (5 - 3)^2} = \sqrt{(2 + 4)^2 + (5 - 3)^2} = \sqrt{(6)^2 + (2)^2} = \sqrt{36 + 4} = \sqrt{40} \approx 6.32
\]

**Length of EL:**
\[
E(2, 5) \quad L(6, 2)
\]
\[
EL = \sqrt{(6 - 2)^2 + (2 - 5)^2} = \sqrt{(4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5.00
\]

**Length of LT:**
\[
L(6, 2) \quad T(0, 0)
\]
\[
LT = \sqrt{(0 - 6)^2 + (0 - 2)^2} = \sqrt{(-6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40} \approx 6.32
\]

**Length of MT:**
\[
M(-4, 3) \quad T(0, 0)
\]
\[
MT = \sqrt{(0 - (-4))^2 + (0 - 3)^2} = \sqrt{(4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5.00
\]

### Step 2: Record the lengths

\[
ME \approx 6.32
\]
\[
EL = 5.00
\]
\[
LT \approx 6.32
\]
\[
MT = 5.00
\]

### Step 3: Check if opposite sides are congruent

- ME ≈ LT (6.32 ≈ 6.32)
- EL = MT (5.00 = 5.00)

Since both pairs of opposite sides are congruent (ME = LT and EL = MT), we can conclude:

**Is this a parallelogram? Type (1 for Yes or 2 for No):**
**1** (Yes)