solve question no 19
Attachments:
Answers
Answered by
1
To prove: OE=OF
given it's a parallelogram so AB and CD are parallel to each other
Now, angle AEO = angle OFC. (internal opposite angles)
Angle EAO = Angle FCO (internal opposite angles)
Angle AOE = Angle FOC (opposite angles at a point of intersection of 2 lines is equal)
so according to AAA(angle-angle-angle ) property traingles OAE and OCF are similar
In similar triangles the ratio of respective sides is same
so OE/OF = OA/OC
Given it's a diagonal and the diagonals in a parallelogram always bisect each other.. so OA=OC, substituting we get,
OE/OF= 1 implies OE= OF
given it's a parallelogram so AB and CD are parallel to each other
Now, angle AEO = angle OFC. (internal opposite angles)
Angle EAO = Angle FCO (internal opposite angles)
Angle AOE = Angle FOC (opposite angles at a point of intersection of 2 lines is equal)
so according to AAA(angle-angle-angle ) property traingles OAE and OCF are similar
In similar triangles the ratio of respective sides is same
so OE/OF = OA/OC
Given it's a diagonal and the diagonals in a parallelogram always bisect each other.. so OA=OC, substituting we get,
OE/OF= 1 implies OE= OF
Similar questions