问题1：构造一个四边形ABCD，其中AB = 3.8 cm，BC = 3.4 cm，CD = 4.5 cm，AD = 5 cm，且∠B= 80°?
解决方案：
The given details are AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, AD = 5 cm and ∠B = 80°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 3.8cm
Step 2: Construct an angle of 80o at B.
Step 3: Taking B as the centre, draw an arc radius of 3.4 cm. Mark this point as C.
Step 4: Taking A as the centre, draw an arc radius of 5 cm. Mark this point as D.
Step 5: Taking C as the centre, draw an arc radius of 4.5 cm intersecting point D.
Step 6: Now join BC, AD, and CD to form a quadrilateral.
问题2：在AB = 8 cm，BC = 8 cm，CD = 10 cm，AD = 10 cm和∠A= 45°的情况下构造四边形ABCD?
解决方案：
The given details are AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and ∠A = 45°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 8cm
Step 2: Construct an angle of 45o at A.
Step 3: Taking A as the centre, draw an arc radius of 10 cm. Mark this point as D.
Step 4: Taking D as the centre, draw an arc radius of 10 cm. Mark this point as C.
Step 5: Taking B as the centre, draw an arc radius 8 cm intersecting point C.
Step 6: Now join AD, DC, and BC to form a quadrilateral.
问题3：构建四边形ABCD，其中AB = 7.7 cm，BC = 6.8 cm，CD = 5.1 cm，AS = 3.6 cm，∠C= 120°?
解决方案：
We have, AB = 7.7 cm, BC = 6.8 cm, CD = 5.1 cm, AS = 3.6 cm and ∠C = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment , DC = 5.1cm
Step 2: Construct an angle of 120° at C.
Step 3: Taking C as the centre, draw an arc radius of 6.8 cm. Mark this point as B.
Step 4: Taking B as the centre, draw an arc radius of 7.7 cm. Mark this point as A.
Step 5: Taking D as the centre, draw an arc radius of 3.6 cm intersecting point A.
Step 6: Now join CB, BA, and DA to form a quadrilateral.
问题4：构造一个四边形ABCD，其中AB = BC = 3 cm，AD = CD = 5 cm，∠B= 120°?
解决方案：
We have, AB = BC = 3 cm, AD = CD = 5 cm and ∠B = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 3cm
Step 2: Construct an angle of 120° at B.
Step 3: Taking B as the centre, draw an arc radius of 3 cm. Mark this point as C.
Step 4: Taking C as the centre, draw an arc radius of 5 cm. Mark this point as D.
Step 5: Taking A as the centre, draw an arc radius of 5 cm intersecting point D.
Step 6: Now join BC, CD, and DA to form a quadrilateral.
问题5：构建一个四边形ABCD，其中AB = 2.8 cm，BC = 3.1 cm，CD = 2.6 cm，DA = 3.3 cm，∠A= 60°?
解决方案：
We have, AB = 2.8 cm, BC = 3.1 cm, CD = 2.6 cm and DA = 3.3 cm and ∠A = 60°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 2.8cm
Step 2: Construct an angle of 60° at A.
Step 3: Taking A as the centre, draw an arc radius of 5.5 cm. Mark this point as D.
Step 4: Taking D as the centre, draw an arc radius of 2.6 cm. Mark this point as C.
Step 5: Taking B as the centre, draw an arc radius of 3.1 cm. Mark this point as C.
Step 6: Now join AD, DC, and CB to form a quadrilateral.
问题6：构造一个四边形ABCD，其中AB = BC = 6 cm，AD = DC = 4.5 cm，且∠B= 120°?
解决方案：
We have, AB = BC = 6 cm, AD = DC = 4.5 cm and ∠B = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 6cm
Step 2: Construct an angle of 120° at B.
Step 3: Taking B as the centre, draw an arc radius of 6 cm. Mark this point as C.
Here, AC is about 10.3 cm in length which is greater than AD + CD = 4.5 + 4.5 = 9cm
We know that sum of the two sides of a triangle is always greater than the third side.
AD + CD < AC
∴ Construction is not possible.
