问题1.构造一个ΔABC，其中BC = 7 cm，∠B= 75°，AB + AC = 13 cm。
解决方案：
Steps of construction:
- Draw a line segment BC base of cm is drawn.
- At point B draw an angle of 75°.
- Cut BD =13cm from BY.
- Join ∠D which intersect BD at A.
- Join AC. Now triangle ABC is the required triangle
问题2.构造一个ABC，其中BC = 8 cm，∠B= 45°，AB – AC = 35 cm。
解决方案：
Steps of construction:
- Draw a line segment BC=8cm.
- At point B, draw angle 45°.
- Cut BD=3.5 from BY.
- Join CD.
- Draw perpendicular bisector of CD, which construct BY at A.
- Join AC. NOW, ABC is the required triangle.
问题3.构造一个ΔABC，其中QR = 6 cm，∠Q= 60°，PR – PQ = 2 cm。
解决方案：
Steps of construction:
- Draw a line segment QR=6cm.
- At point Q draw angle 60°.
- Extend PQ to Y’.
- Cut QS =2cm from QY’.
- Join RS.
- Draw perpendicular bisector of RS which intersect QY at P.
- Join PR. Now, PQR is the required triangle.
问题4.构造一个ΔXYZ，其中∠Y= 30°，∠Y= 90°，XY + YZ + ZX = 11 cm。
解决方案：
Steps of construction:
- Draw a line segment AB=11cm.
- At point A draw ∠BAP=30°.
- At point B draw angle 90°.
- Draw the bisector of ∠BAP and ∠ABR which intersect each other at X.
- Join AX and BX.
- Draw perpendicular bisector of AX and BX which intersect AB on Y and Z respectively.
- Join XY and XZ. Then XYZ is the required triangle.
问题5.构造一个直角三角形，其底边为12厘米，其斜边和另一边的总和为18厘米。
解决方案：
Steps of construction:
- Draw a line segment of BC=12cm.
- At point B draw angle b=90°
- Cut BD =18cm.
- Join CD.
- Draw perpendicular bisector of CD which intersect BD at point A.
- Join AC. Now ABC is the required triangle.
