Question

In a figure O i s the midpoint of AB and CD. prove that AC=BD

Answer 1

Answer:

OB= OA (O is the mid-point of AB)

∠AOC=∠BOD [V.O.A.]

OC=OD (O is the mid-point of CD)

By SAS rule,

 ΔAOC≅ΔBOD

⇒AC=BD [BY CPCT]

 

Step-by-step explanation:

Answer 2

Given:

• O is the mid-point of AB and CD.

To prove:
AC = BD

Step by step explanation:

→ Basic concept used: Congruency of triangles.

In ΔAOC and ΔBOD,
OA = OB           .................... (O is the midpoint of AB)
∠AOC = ∠BOD        ............ (Vertically opposite angles)
OC = OD          ..................... (O is the midpoint of CD)
By SAS (Side-angle-side) property,
ΔAOC ≅ ΔBOD
By CPCT (corresponding parts of congruent triangles)
AC = BD.
Hence proved.

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