Question

Construct an angle 75.
Construct a bisector of above angle and write justification.(37.5)
Draw a line segment XY=10cm and quadrisect it.
Construct a PQR where QR =3cm, ∠PQR= 45and
QP-PR = 2cm.Justify the construction.
Construct a right angled triangle ,whose base is 3.5cm and sum of hypotenuse and other side is 5.5cm.Justify the construction.

Answer 1

Given  A line segment XY=10cm and quadrisect it.

To Find : quadrisect the line

Solution:

Construct an angle 75.

Construct a bisector of above angle and write justification

Step 1 : Draw a line segment AB

Step 2 : Draw  an angle of 75° using protector at A on AB and label another end of C

Step 3 : Using compass Draw an arc taking A as center , intersecting AB & AC at M & N

Step 4 : Taking some compass width Taking M as center draw an arc

Step 5 : Keeping compass width same as in step 4 , now taking N as center draw an arc intersecting arc drawn in step 4 at O

Step 6 : join AO & extend

AO is angle bisector of ∠CAB

∠CAO = ∠BAO =  37.5°

Draw a line segment XY=10cm and quadrisect it.

method 1 :  Using perpendicular bisector :

Step 1 : Draw a line segment  XY  = 10 cm

Step 2 : Using suitable compass width and taking X as center draw arcs on both sides

Step 3 : Keeping compass width same and taking Y as center Draw arcs such that it intersects arc drawn in previous steps at A & B.

Step 4 : Join A & B , intersecting XY at M

Repeat step from 2 to 4  using X & M as center   and  Y & M as center

Method 2 :

Step 1 : Draw a line segment XY = 10 cm

Step 2 : Draw an acute angle at X on YX

Step 3 : Mark 4 points on angle drawn at equal distance , one by one

Step 4 : Join 4th point with Y

Step 5 : one by one Draw  lines parallel to the line drawn passing through 1st  2nd & 3rd point and intersecting   XY .

Construct a PQR where QR =3cm, ∠PQR= 45and  QP-PR = 2cm

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