Question

Draw a triangle PQR in which QR= 5.5 cm , angle Q = 30 deg and QR – PQ = 2 cm. Also write the

steps of constructionDraw a triangle PQR in which QR= 5.5 cm , angle Q = 30 deg and QR – PQ = 2 cm. Also write the

steps of construction​

Answer 1

Answer:

Construct a ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 35 cm.

Solution:

Steps of Construction:

Step I : Draw BX¯¯¯¯¯¯¯¯.

Step II : Along BX¯¯¯¯¯¯¯¯, cut off a line segment BC = 8 cm.

Step III : At B, construct ∠CBY = 45°

Step IV : From BX¯¯¯¯¯¯¯¯, cut off BD = 3.5 cm (= AB – AC)

Step V : Join DC.

Step VI : Draw PQ, perpendicular bisector of DC, which intersects BY¯¯¯¯¯¯¯¯ at A.

Step VII: Join AC.

Construct a ∆ ABC in which QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm.

Solution:

Steps of Construction:

Step I : Draw QX¯¯¯¯¯¯¯¯.

Step II : Along QX¯¯¯¯¯¯¯¯, cut off a line segment QR = 6 cm.

Step III : Construct a line YQY’ such that ∠RQY = 60°.

Step IV : Cut off QS = 2 cm (= PR – PQ) on QY’.

Step V : Join SR.

Step VI : Draw MN, perpendicular bisector of SR, which intersects QY at P.

Step VII: Join PR.

Construct a ∆ XYZ in which ∠Y = 30°, ∠Y = 90° and XY + YZ + ZX = 11 cm.

Solution:

Steps of Construction:

Step I : Draw a line segment AB = 11 cm = (XY+YZ + ZX)

Step II : Construct ∠BAP = 30°

Step III : Construct ∠ABQ = 90°

Step IV : Draw AR, the bisector of ∠BAP.

Step V : Draw BS, the bisector of ∠ABQ. Let AR and BS intersect at X.

Step VI : Draw perpendicular bisector of AX¯¯¯¯¯¯¯¯, which intersects AB at Y.

Step VII: Draw perpendicular bisector of XB¯¯¯¯¯¯¯¯, which intersects AB at Z.

Step VIII: Join XY and XZ.