Question

6. ABC is a right angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (the dotted lines are drawn additionally to help you). cbse class 8 maths chapter 3 understanding quadrilateral. exercise 3.4

Answer 1

Answer:

Between Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).

∠ AOD =∠ BOC....Vertically opposite angle

∴ By SAS test Δ AOD & Δ BOC are congruent.

So AD=BC....(i)

similarly, between Δ AOB & Δ DOC we have AO=CO (given), BO=OD (by Construction)

∠ AOB =∠ DOC

∴ By SAS test Δ AOB & Δ DOC are congruent.

So AB=DC.....(ii)

Also ∠ ABC=90

o

....(iii)

∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.

So the diagonals AC & BD are equal and bisect each other at O.

∴ OA=OB=OC=OD.

i.e O is equidistant from A, B & C.

Step-by-step explanation:

I hope this helps you dear

Answer 2

so AB=DCandAD=BC

angleA=angleB=angleC=angleD=90degree angle

the diagonal of a rectangle bisect each other

so; OA=OCandOB=OD

In addition the diagonal of a rectangle are of equal length

so; AC=BD

let us verify this property

in angle ABCand angleBAD

AB=AB

angleA=angleB

AD=BC

angleABC=angleBAD

so; AC=BD

hence the diagonal of a rectangle are equal in length