5. A rectangle has vertices at points $$ (0,0),(2 c, 0),(2 c, c),(0, c) $$. Select all the points that lie on the sides of the rectangle. $$ \square $$ A. $$ (0,2 c) $$ $$ \square $$ B. $$ (c, c) $$ $$ \square $$ C. $$ (2 c, 2 c) $$ $$ \square $$ D. $$ (c, 0) $$ $$ \square $$ E. $$ (c, 2 c) $$

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The rectangle has vertices at $$ (0,0) $$, $$ (2c,0) $$, $$ (2c,c) $$, and $$ (0,c) $$.

This means the sides of the rectangle are:
- The bottom side: $$ y = 0 $$ for $$ 0 \leq x \leq 2c $$
- The top side: $$ y = c $$ for $$ 0 \leq x \leq 2c $$
- The left side: $$ x = 0 $$ for $$ 0 \leq y \leq c $$
- The right side: $$ x = 2c $$ for $$ 0 \leq y \leq c $$

Now, consider each point:

1. **Option A: $$ (0, 2c) $$**
   - Here, $$ x = 0 $$ could lie on the left side, but for the left side the $$ y $$-coordinate must satisfy $$ 0 \leq y \leq c $$. Since $$ 2c > c $$, this point is not on the left side.
   - **Conclusion:** Not on the rectangle.

2. **Option B: $$ (c, c) $$**
   - Here, $$ y = c $$ and $$ x = c $$, which satisfies the top side criteria $$ 0 \leq x \leq 2c $$.
   - **Conclusion:** Lies on the top side.

3. **Option C: $$ (2c, 2c) $$**
   - Here, $$ x = 2c $$ suggests it could lie on the right side, but the right side requires $$ 0 \leq y \leq c $$. Since $$ 2c > c $$, it is not on the right side.
   - **Conclusion:** Not on the rectangle.

4. **Option D: $$ (c, 0) $$**
   - Here, $$ y = 0 $$ and $$ x = c $$ fits the bottom side $$ 0 \leq x \leq 2c $$.
   - **Conclusion:** Lies on the bottom side.

5. **Option E: $$ (c, 2c) $$**
   - Here, $$ x = c $$ and $$ y = 2c $$. The point does not satisfy any side criterion because the only horizontal lines are $$ y = 0 $$ and $$ y = c $$.
   - **Conclusion:** Not on the rectangle.

The points that lie on the sides of the rectangle are thus:

$$ \boxed{(c,c) 	ext{ and } (c,0)} $$
  
Which corresponds to options B and D.
Points on the rectangle's sides are $$ (c, c) $$ and $$ (c, 0) $$.

5. A rectangle has vertices at points \( (0,0),(2 c, 0),(2 c, c),(0, c) \). Select all the points that lie on the sides of the rectangle. \( \square \) A. \( (0,2 c) \) \( \square \) B. \( (c, c) \) \( \square \) C. \( (2 c, 2 c) \) \( \square \) D. \( (c, 0) \) \( \square \) E. \( (c, 2 c) \)

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