. In the given figure, ABCD is a parallelogram in which diagonals AC and BD intersect at O. A line segment LM is drawn passing through O. Prove that LO = OM.
Answers
Answered by
86
Given ABCD is a parallelogram and AC,
BD is the diagonals intersecting at O.
Hence OA = OC and OB = OD [Since diagonals bisect each other]
Consider, ΔAOL and ΔCOM ∠AOL = ∠COM [Vertically opposite angles]
OA = OC [Given]
∠OAL = ∠OCM [Alternate angles]
∴ ΔAOL ≅ ΔCOM [By ASA Congruence criterion]
Hence OL = OM (CPCT) .
Answered by
4
Answer:
Given ABCD is a parallelogram and AC,
BD is the diagonals intersecting at O.
Hence OA = OC and OB = OD [Since diagonals bisect each other]
Consider, ΔAOL and ΔCOM ∠AOL = ∠COM [Vertically opposite angles]
OA = OC [Given]
∠OAL = ∠OCM [Alternate angles]
∴ ΔAOL ≅ ΔCOM [By ASA Congruence criterion]
Hence OL = OM (CPCT) .
Similar questions
Math,
1 month ago
English,
1 month ago
Hindi,
1 month ago
Math,
3 months ago
India Languages,
9 months ago