Question

step by step explaination:​

Answer 1

Answer:

∆ABO≈ ∆AOD

So,AB=AD

By CPCTC

Similarly

∆BOC≈∆COD

So, BC=DC

By CPCTC

Answer 2

Question:

In □ABCD, diagonal AC is perpendicular bisector of seg BD. Prove that -

1) AB = AD

2) BC = DC

Answer:

1) Seg AB ≅ Seg AD

2) Seg BC ≅ Seg DC

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

1)

We have given that, In □ABCD,

Diagonal AC is perpendicular bisector of seg BD.

∴ AC ⊥ BD

∴ m∟AOB = m∟AOD = 90°

∴ ∠AOB ≅ ∠AOD - - ( 1 )

Now,

Seg AC is the bisector of seg BD.

∴ Seg BO ≅ Seg DO - - ( 2 )

Now, in △AOB & △AOD,

Seg BO ≅ Seg DO - - [ From ( 2 ) ]

∠AOB ≅ ∠AOD - - [ From ( 1 ) ]

Seg AO ≅ Seg AO - - [ Common side ]

∴ △AOB ≅ △AOD - - [ S - A - S test ]

∴ Seg AB ≅ Seg AD - - [ c. s. c. t. ]

Hence proved!

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2)

Now,

m∟BOC = m∟DOC = 90° - - [ AC ⊥ BD ]

∴ ∠BOC ≅ DOC - - ( 3 )

Now, in △BOC & △DOC,

Seg BO ≅ Seg DO - - [ From ( 2 ) ]

∠BOC ≅ DOC - - [ From ( 3 ) ]

Seg OC ≅ Seg OC - - [ Common side ]

∴ △BOC ≅ △DOC - - [ S - A - S test ]

∴ Seg BC ≅ Seg DC - - [ c. s. c. t. ]

Hence proved!