问题1：构造一个四边形ABCD，其中AB = 3.8厘米，BC = 3.0厘米，AD = 2.3厘米，AC = 4.5厘米，BD = 3.8厘米?
解决方案：
We have, AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AC = 6cm.
Step 2: Taking A as the centre, draw an arc of radius = 3.8 cm. Mark that point as B.
Step 3: Taking C as the centre, draw an arc of radius = 3 cm intersecting point B.
Step 4: Taking B as the centre, draw an arc of radius = 3.8 cm. Mark that point as D.
Step 5: Taking A as the centre, draw an arc of radius = 2.3 cm intersecting point D.
Step 6: Now join AB, BD, AD, and DC to form a quadrilateral.
问题2：构建四边形ABCD，其中BC = 7.5 cm，AC = AD = 6 cm，CD = 5 cm和BD = 10 cm?
解决方案：
We have, BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AC = 6cm.
Step 2: Taking A as the centre, draw an arc of radius = 6 cm. Mark that point as D.
Step 3: Taking C as the centre, draw an arc of radius = 5 cm intersecting point D.
Step 4: Taking D as the centre, draw an arc of radius = 10 cm. Mark that point as B.
Step 5: Taking C as the centre, draw an arc of radius = 7.5 cm intersecting point B.
Step 6: Now join AD, CD, DB, and AB to form a quadrilateral.
问题3：当AB = 3 cm，CD = 3 cm，DA = 7.5 cm，AC = 8 cm和BD = 4 cm时构造四边形ABCD?
解决方案：
We have, AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.
Consider a triangle ABD,
Now, AB + BD = 3 + 4 = 7 cm
Note: Sum of lengths of two sides of a triangle is always greater than the third side.
∴ The construction is not possible.
问题4：在AD = 3.5 cm，BC = 2.5 cm，CD = 4.1 cm，AC = 7.3 cm和BD = 3.2 cm的情况下构造四边形ABCD?
解决方案：
We have, AD = 3.5 cm, BC = 2.5 cm, CD = 4.1 cm, AC = 7.3 cm and BD = 3.2 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment CD = 4.1cm
Step 2: Taking C as the centre, draw an arc of radius = 7.3 cm. Mark that point as A.
Step 3: Taking D as the centre, draw an arc of radius = 3.5 cm intersecting point A.
Step 4: Taking D as the centre, draw an arc of radius = 3.2 cm. Mark that point as B.
Step 5: Taking C as the centre, draw an arc of radius = 2.5 cm intersecting point B.
Step 6: Now join CA, DA, DB, CB, and AB to form a quadrilateral.
问题5：在AD = 5 cm，AB = 5.5 cm，BC = 2.5 cm，AC = 7.1 cm和BD = 8 cm的情况下构造四边形ABCD?
解决方案：
We have, AD = 5 cm, AB = 5.5 cm, BC = 2.5 cm, AC = 7.1 cm and BD = 8 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 5.5 cm
Step 2: Taking B as the centre, draw an arc of radius = 2.5 cm. Mark that point as C.
Step 3: Taking A as the centre, draw an arc of radius = 7.1 cm intersecting point C.
Step 4: Taking B as the centre, draw an arc of radius = 8 cm. Mark that point as D.
Step 5: Taking A as the centre, draw an arc of radius = 5 cm intersecting point D.
Step 6: Join the line segments BC, AC, BD, AD, and CD to form a quadrilateral.
问题6：构建四边形ABCD，其中BC = 4 cm，CA = 5.6 cm，AD = 4.5 cm，CD = 5 cm，BD = 6.5 cm?
解决方案：
We have, BC = 4 cm, CA = 5.6 cm, AD = 4.5 cm, CD = 5 cm and BD = 6.5 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment BC = 4cm
Step 2: Taking B as the centre, draw an arc of radius = 6.5 cm. Mark that point as D.
Step 3: Taking C as the centre, draw an arc of radius = 5 cm intersecting point D.
Step 4: Taking C as the centre, draw an arc of radius = 5.6 cm. Mark that point as A.
Step 5: Taking D as the centre, draw an arc of radius = 4.5 cm intersecting point A.
Step 6: Join the line segments BD, CD, CA, DA, and AB to form a quadrilateral.
