3. Construct a quadrilateral $$ A B C D $$ in which $$ \mathrm{cm}, B C=3 \mathrm{~cm}, A D=6 \mathrm{~cm}, A C=4 \mathrm{~cm} $$ and $$ B D=7 $$ cm.

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To construct the quadrilateral $$ ABCD $$ with the given side lengths, we can follow these steps:

1. **Draw Segment $$ BC $$**:
   - Start by drawing a line segment $$ BC $$ that is $$ 3 \, 	ext{cm} $$ long.

2. **Draw Circle for Point $$ A $$**:
   - From point $$ B $$, draw a circle with a radius of $$ 6 \, 	ext{cm} $$ (since $$ AD = 6 \, 	ext{cm} $$).
   - From point $$ C $$, draw another circle with a radius of $$ 4 \, 	ext{cm} $$ (since $$ AC = 4 \, 	ext{cm} $$).
   - The intersection of these two circles will give you point $$ A $$.

3. **Draw Circle for Point $$ D $$**:
   - From point $$ B $$, draw a circle with a radius of $$ 7 \, 	ext{cm} $$ (since $$ BD = 7 \, 	ext{cm} $$).
   - From point $$ A $$, draw a circle with a radius of $$ 6 \, 	ext{cm} $$ (since $$ AD = 6 \, 	ext{cm} $$).
   - The intersection of these two circles will give you point $$ D $$.

4. **Connect the Points**:
   - Finally, connect points $$ A $$, $$ B $$, $$ C $$, and $$ D $$ to form the quadrilateral $$ ABCD $$.

This construction ensures that all the given lengths are satisfied. The quadrilateral $$ ABCD $$ will have the sides $$ AB $$, $$ BC $$, $$ CD $$, and $$ DA $$ with the specified lengths.
To construct quadrilateral $$ ABCD $$ with sides $$ BC = 3 \, 	ext{cm} $$, $$ AD = 6 \, 	ext{cm} $$, $$ AC = 4 \, 	ext{cm} $$, and $$ BD = 7 \, 	ext{cm} $$, follow these steps: 1. Draw segment $$ BC $$ of $$ 3 \, 	ext{cm} $$. 2. From point $$ B $$, draw a circle with radius $$ 6 \, 	ext{cm} $$. 3. From point $$ C $$, draw a circle with radius $$ 4 \, 	ext{cm} $$. 4. The intersection of these circles is point $$ A $$. 5. From point $$ B $$, draw a circle with radius $$ 7 \, 	ext{cm} $$. 6. From point $$ A $$, draw a circle with radius $$ 6 \, 	ext{cm} $$. 7. The intersection of these circles is point $$ D $$. 8. Connect points $$ A $$, $$ B $$, $$ C $$, and $$ D $$ to form quadrilateral $$ ABCD $$. This construction ensures all given side lengths are satisfied.

3. Construct a quadrilateral \( A B C D \) in which \( \mathrm{cm}, B C=3 \mathrm{~cm}, A D=6 \mathrm{~cm}, A C=4 \mathrm{~cm} \) and \( B D=7 \) cm.

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