Construct a parallelogram ABCD  AB=4.5 AC=4.8 BD= 6.4

To construct the parallelogram ABCD with the given dimensions, follow these steps:

### Given Data:
- \( AB = 4.5 \) units
- \( AC = 4.8 \) units
- \( BD = 6.4 \) units

We will assume that the diagonal \( AC \) is one diagonal of the parallelogram, and \( BD \) is the other diagonal.

### Steps to Construct the Parallelogram:

1. **Draw Line Segment AB:**
   - Use a ruler to draw line segment \( AB = 4.5 \) units.

2. **Draw Diagonal AC:**
   - From point \( A \), draw line segment \( AC = 4.8 \) units. Mark point \( C \) at the end of the segment.

3. **Draw Diagonal BD:**
   - Use a compass to draw the diagonal \( BD = 6.4 \) units.
   - Place the compass at point \( A \) and draw an arc with a radius of half the length of diagonal \( BD \) (which is \( \frac{6.4}{2} = 3.2 \) units).
   - Without changing the compass width, place the compass at point \( C \) and draw another arc.
   - The intersection of these arcs gives point \( O \), which is the midpoint of diagonals \( AC \) and \( BD \).

4. **Mark Point D:**
   - From point \( O \), set the compass to a radius of \( 3.2 \) units, and from \( O \), draw an arc passing through point \( B \). This will locate point \( D \) opposite to \( B \).

5. **Complete the Parallelogram:**
   - Join points \( B \) and \( D \), and points \( A \) and \( D \).
   - You should now have parallelogram ABCD, with \( AB = 4.5 \), diagonal \( AC = 4.8 \), and diagonal \( BD = 6.4 \).

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Would you like further details or have any questions on this construction? 

Here are 5 follow-up questions related to this construction:
1. How would you verify that ABCD is a parallelogram using geometric properties?
2. What is the area of the parallelogram ABCD if we know the height?
3. How can you prove that the diagonals bisect each other in this parallelogram?
4. What type of parallelogram would this be if \( AB \) and \( AC \) were equal?
5. How do the properties of parallelograms help in determining the length of other sides?

**Tip**: In a parallelogram, opposite sides are equal and parallel, and diagonals bisect each other.

Construct a parallelogram ABCD with AB=4.5, AC=4.8, and BD=6.4.

Learn how to construct a parallelogram ABCD with given side lengths AB=4.5, AC=4.8, and diagonal BD=6.4. This tutorial covers key geometry concepts such as diagonal bisectors and parallelogram properties, suitable for Grades 8-10.

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