第 9 类 RD Sharma 解决方案 - 第 17 章构造 - 练习 17.3
问题 1. 构造一个 Δ ABC，其中 BC = 3.6 cm，AB + AC = 4.8 cm，∠B = 60°。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 8.6cm.
2. Draw ∠B = 60°.
3. Now, with centre B and radius = 4.8cm, draw an arc that intersects line XB at point D.
4. Join DC.
5. Now, draw a perpendicular of DC that intersects DB at point A.
6. Join AC.
So, Δ ABC is the triangle.
问题 2. 构造一个 ΔABC，其中 AB + AC = 5.6 cm，BC = 4.5 cm，∠B = 45°。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 4.5cm.
2. Draw ∠B = 45°.
3. Now, with centre B and radius = 5.6cm, draw an arc that intersect line BC at point O.
4. Join DC.
5. Now, draw the perpendicular bisector of DC that intersect line BC at point A.
6.Join AC.
So, Δ ABC is the triangle.
问题 3. 构造一个 Δ ABC，其中 BC = 3.4 cm，AB - AC = 1.5 cm，∠B = 45°。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 3.4cm.
2. Draw ∠B = 45°.
3. Now, with centre B and radius = 1.5cm, draw an arc that intersect line BX at point D.
4. Join DC.
5. Now, draw a perpendicular bisector of DC that intersects line BX at point A.
6. Join AC.
So, Δ ABC is the triangle.
问题 4. 仅使用尺子和圆规，构造一个 ΔABC，给定底边 BC = 7 cm，∠ABC = 60° 和 AB + AC = 12 cm。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 7cm.
2. Draw ∠B = 60°
3. Now, with centre B and radius = 12cm, draw an arc that intersects line BX at point D.
4. Join DC.
5. Now, draw the perpendicular bisector of DC that intersects line BD at point A.
6. Join AC.
So, Δ ABC is the triangle.
问题 5. 做一个三角形，其周长为 6.4 厘米，底角为 60° 和 45°。
解决方案：
Steps of Construction:
1. Draw a line segment XY = 6.4cm.
2. Draw the angle bisectors of∠EYY = 45°
3. Now, draw the angle bisector of∠BXY and ∠EYX that intersect each other at point A.
4. Draw the perpendicular bisector of lines AX and AY that intersect line XY at points B and C.
5. Join AB and AC.
So, Δ ABC is the triangle.
问题 6. 仅使用尺子和圆规，根据以下数据构造 Δ ABC：
AB + BC + CA = 12 厘米，∠B = 45° 和∠C = 60°。
解决方案：
Steps of Construction:
1. Draw a line segment XY = 12cm.
2. Draw∠X = ∠B = 45° and ∠Y = ∠C = 60°
3. Now, draw the angle bisectors of angles of DXY and EYX that intersects each other at point A.
4. Draw the perpendicular bisector of AX and AY that intersect line XY at points B and C.
5. Join AB and AC.
So, Δ ABC is the triangle.
问题 7. 做一个直角三角形，其周长等于 10 厘米，一个锐角等于 60°。
解决方案：
Steps of Construction:
1. Draw a line segment XY = 10cm.
2. Draw ∠X = ∠B = 90 and ∠Y = ∠C = 60
3. Now, draw the angle bisector of ∠DXY and ∠EXY that intersect each other at point A.
4. Draw the perpendicular bisectors of AX and AY which intersects line XY at points B and C.
5. Join AB and AC.
So, Δ ABC is the triangle.
问题 8. 构造一个三角形 ABC，使得 BC = 6 cm，AB = 6 cm，中位数 AD = 4 cm。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 6 cm
2. Now, take mid-point D of line BC.
3. With centre B and D and radius 6cm and 4cm, draw two arcs that intersects each other at point A.
4. Now, join AB, AD, and AC.
So, Δ ABC is the triangle.
问题 9. 作一个直角三角形 ABC，其底边 BC 为 6 cm，斜边 AC 与另一边 AB 之和为 10 cm。
解决方案：
Steps of Construction:
1. Draw a line segment BC = 6cm.
2. Now, at point B draw and angel of 90°
3. Now, with centre B and radius = 10cm, draw an arc that intersect line XB at point D.
4. Join DC.
5. Draw the perpendicular bisector of DC that intersects line DB at point A.
6. Join AC.
So, Δ ABC is the triangle.
问题 10. 构造一个三角形 XYZ，其中∠Y = 30°，∠Z = 90°，XY + YZ + ZX = 11。
解决方案：
Steps of Construction:
1. Draw a line segment AB = 11cm.
2. Draw ∠A =∠Y = 30 and ∠B = ∠Z = 90
3. Now, draw the angle bisectors of ∠DAB and ∠EBA that intersect each other at point X.
4. Draw the perpendicular bisectors of XA and XB that intersect line AB at points Y and Z.
5. Join XY and XZ.
So, Δ XYZ is the triangle.
