In the given figure- AB CD and AB - CD- -3 MARKS-Prove that- i - AOB - DOCii AO - DOiii BO - CO

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Standard VIII

Mathematics

ASA Postulate

In the given ...

Question

In the given figure, $A B ∥ C D$ and AB = CD. [3 MARKS]

Prove that: (i) $Δ A O B ≅ Δ D O C$

(ii) AO = DO

(iii) BO = CO

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Solution

Each proof: 1 Mark

In $Δ A O B$ and $Δ C O D$

$A B = C D$ [Given]

$∠ B A O = ∠ C D O$ [Alternate angles; as $A B ∥ C D$ ]

$∠ A B O = ∠ D C O$ [Alternate angles; as $A B ∥ C D$ ]

(i) $∴ Δ A O B ≅ Δ D O C$ [A.S.A congruency criteria]

(ii) $A O = D O$ [Corresponding sides of congruent triangles]

also, (iii) $B O = C O$ [Corresponding sides of congruent triangles]

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In the given figure, AB∥CD and AB = CD. [3 MARKS] Prove that: (i) ΔAOB≅ΔDOC (ii) AO = DO (iii) BO = CO

In the given figure, $A B ∥ C D$ and AB = CD. [3 MARKS]

Prove that: (i) $Δ A O B ≅ Δ D O C$

(ii) AO = DO

(iii) BO = CO