OM is perpendicular to AB in the diagram. Prove that M is the mid poi

1.	OM is perpendicular to AB in the diagram. Prove that M is the mid point of AB.
Answer» OA = OB ∴ ∆ OAB is an isosceles triangle. ∴ ∠A = ∠B When ∆ OMA and ∆ OMB are considered, OM is the common side ∠AMO = ∠BMO = 90 ∠AOM = ∠BOM One side of the triangle and angles at the ends of sides are equal. So the other two sides are also equal. ∴ AM = MB ∴ M is the midpoint of AB.

OM is perpendicular to AB in the diagram. Prove that M is the mid point of AB.

Answer»

OA = OB

∴ ∆ OAB is an isosceles triangle.

∴ ∠A = ∠B

When ∆ OMA and ∆ OMB are considered, OM is the common side

∠AMO = ∠BMO = 90 ∠AOM = ∠BOM

One side of the triangle and angles at the ends of sides are equal. So the other two sides are also equal.

∴ AM = MB

∴ M is the midpoint of AB.