Question

s it possible to construct a square in which the measure of one diagonal is given? Give reason for your answer.

Answer 1

Answer:

Step-by-step explanation:

Given : Diagonal=6 cm.

Steps for construction

Step 1 : Draw the rough diagram and mark the given measures.

Step 2 : Draw a line segment AC=6 cm.

Step 3 : Construct a perpendicular bisector  

XY

 of  

AC

.

Step 4 :  

XY

 intersects  

AC

 at O. We get OC=AO=3 cm.

Step 5 : With O as centre draw two arcs of radius 3 cm cutting the line  

XY

 at points B and D.

Step 6 : Join  

AB

,  

BC

,  

CD

 and  

DA

.

ABCD is the required square

Answer 2

Ans:Now draw perpendicular bisector of AC. Let it intersect AC at point O. With O as centre and radius equal to half of the length of the diagonal (2.5 cm) draw two arcs on either side of AC on the perpendicular bisector. Mark the point of intersections of the arcs and perpendicular bisectors as B and C.