问题1：构造一个四边形ABCD，其中AB = 6 cm，BC = 4 cm，CD = 4 cm，∠B= 95°，∠C= 90°?
解决方案：
We have, AB = 6 cm, BC = 4 cm, CD = 4 cm, ∠B = 95° and ∠C = 90°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment BC = 4cm
Step 2: Construct an angle of 95° at B.
Step 3: Taking B as the centre, draw an arc radius of 6 cm. Mark this point as A.
Step 4: Construct an angle of 90° at C.
Step 5: Taking C as the centre, draw an arc radius of 4 cm. Mark this point as D.
Step 6: Now join the line segments BA, CD, and AD to form a quadrilateral.
问题2：构造一个四边形ABCD，其中AB = 4.2cm，BC = 3.6 cm，CD = 4.8 cm，∠B= 30°，∠C= 150°?
解决方案：
The given details are AB = 4.2cm, BC = 3.6 cm, CD = 4.8 cm, ∠B = 30° and ∠C = 150°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment BC = 3.6cm
Step 2: Construct an angle of 30° at B.
Step 3: Taking B as the centre, draw an arc radius of 4.2 cm. Mark this point as A.
Step 4: Construct an angle of 150° at C.
Step 5: Taking C as the centre, draw an arc radius of 4.8 cm. Mark this point as D.
Step 6: Now join BA, CD, and AD to form a quadrilateral.
问题3：构造一个四边形的PQRS，其中PQ = 3.5 cm，QR = 2.5 cm，RS = 4.1 cm，∠Q= 75°，∠R= 120°?
解决方案：
The given details are PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment QR = 2.5cm
Step 2: Construct an angle of 75° at Q.
Step 3: Taking Q as the centre, draw an arc radius of 3.5 cm. Mark this point as P.
Step 4: Construct an angle of 120° at R.
Step 5: Taking R as the centre, draw an arc radius of 4.1 cm. Mark this point as S.
Step 6: Now join QP, RS, and PS to form a quadrilateral.
问题4：在BC = 6.6 cm，CD = 4.4 cm，AD = 5.6 cm ConstructD = 100°和∠C= 95的情况下构造四边形ABCD?
解决方案：
We have, BC = 6.6 cm, CD = 4.4 cm, AD = 5.6 cm ∠D = 100° and ∠C = 95
Steps to construct a quadrilateral:
Step 1: Draw a line segment DC = 4.4cm
Step 2: Construct an angle of 100° at D.
Step 3: Taking D as the centre, draw an arc radius of 5.6 cm. Mark this point as A.
Step 4: Construct an angle of 95° at C.
Step 5: Taking C as the centre, draw an arc radius of 6.6 cm. Mark this point as B.
Step 6: Now join DA, CB, and AB to form a quadrilateral.
问题5：构建一个四边形ABCD，其中AD = 3.5厘米，AB = 4.4厘米，BC = 4.7厘米，∠A= 125°，∠B= 120°?
解决方案：
The given details are AD = 3.5 cm, AB = 4.4 cm, BC = 4.7 cm, ∠A = 125° and ∠B = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line AB = 4.4cm
Step 2: Construct an angle of 125° at A.
Step 3: Taking A as the centre, draw an arc radius of 3.5 cm. Mark this point as D.
Step 4: Construct an angle of 120° at B.
Step 5: Taking B as the centre, draw an arc radius of 4.7 cm. Mark this point as C.
Step 6: Now join AD, BC, and CD to form a quadrilateral.
问题6：构造一个四边形的PQRS，其中∠Q= 45°，∠R= 90°，QR = 5 cm，PQ = 9 cm，RS = 7 cm?
解决方案：
We have, ∠Q = 45° and ∠R = 90°, QR = 5 cm, PQ = 9 cm and RS = 7 cm.
Steps to construct a quadrilateral:
Step 1: Draw a line segment QR = 5cm
Step 2: Construct an angle of 45° at Q.
Step 3: Taking Q as the centre, draw an arc radius of 9 cm. Mark this point as P.
Step 4: Construct an angle of 90° at R.
Step 5: Taking R as the centre, draw an arc radius of 7 cm. Mark this point as S.
Step 6: Now join the line segments QP, RS.
Since the line segment, QP and RS are not intersecting at each other, a quadrilateral cannot be formed.
问题7：构建一个四边形ABCD，其中AB = BC = 3 cm，AD = 5 cm，∠A= 90°，∠B= 105°?
解决方案：
We have, AB = BC = 3 cm, AD = 5 cm, ∠A = 90° and ∠B = 105°.
Steps to construct a quadrilateral:
Step 1: Draw a line AB = 3cm
Step 2: Construct an angle of 90° at A.
Step 3: Cut an arc of radius 5cm with A as the centre to mark that point as D.
Step 4: Construct an angle of 105° at B.
Step 5: Cut an arc of radius 3cm with B as the centre to mark that point as C.
Step 6: Now join AD, BC, and CD
问题8：构造一个四边形BDEF，其中DE = 4.5 cm，EF = 3.5 cm，FB = 6.5 cm，∠F= 50°和∠E= 100°?
解决方案：
We have, DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, ∠F = 50° and ∠E = 100°.
Steps to construct a quadrilateral:
Step 1: Draw a line EF = 3.5cm
Step 2: Construct an angle of 100° at E.
Step 3: Cut an arc of radius 4.5cm with E as the centre to mark that point as D.
Step 4: Construct an angle of 50° at F.
Step 5: Cut an arc of radius 6.5cm with F as the centre to mark that point as B.
Step 6: Now join DE, FB, and DB
