In the given figure- if AB - BC and - BAO - - BCO - 90- then prove that triangle ABO triangle CBO are congruent-

In ABO and CBO (i) ∠ BAO = ∠ CAO = 90^∘ ........ (given) (ii) BO = BO nbsp;.........(common side) (iii) AB nbsp;= BC........ (given) (1 Mark) ⇒ ABO ≅ C ...

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Standard VII

Mathematics

RHS Congruence Criterion

In the given ...

Question

In the given figure, if AB = BC and $∠ B A O = ∠ B C O = 90^{\circ}$ , then prove that triangle ABO triangle CBO are congruent.

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Solution

In $△ A B O$ and $△ C B O$

(i) $∠ B A O = ∠ C A O = 90^{\circ}$ ........ (given)

(ii) BO = BO .........(common side)

(iii) AB = BC........ (given) (1 Mark)

$\Rightarrow △ A B O ≅ △ C B O$ ........ (RHS Postulate)
$\Rightarrow$ OA = OC.......(cpct)
$\Rightarrow$ $∠ A B O = ∠ C B O = 60^{\circ}$ ........(cpct) (1 Mark)

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In the given figure, if AB = BC and ∠BAO=∠BCO=90∘, then prove that triangle ABO triangle CBO are congruent.

In △ABO and △CBO (i) ∠BAO=∠CAO=90∘ ........ (given) (ii) BO = BO .........(common side) (iii) AB = BC........ (given) (1 Mark) ⇒△ABO≅△CBO ........ (RHS Postulate) ⇒ OA = OC.......(cpct) ⇒ ∠ABO=∠CBO=60∘ ........(cpct) (1 Mark)

In the given figure, if AB = BC and $∠ B A O = ∠ B C O = 90^{\circ}$ , then prove that triangle ABO triangle CBO are congruent.