In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If $A O = 2 C O$ and $B O = 2 D O$ ; Then,
$Δ A O B$ is similar to $Δ C O D$

True

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False

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Solution

The correct option is A True
Given: $A O = 2 C O$ or $\frac{A O}{C O} = 2$
Also given, $B O = 2 D O$ or $\frac{B O}{D O} = 2$
In $△ A O B$ and $△ C O D$ , we know
$∠ A O B = ∠ C O D$
$\frac{A O}{C O} = \frac{B O}{D O}$
Thus, $△ A O B \sim △ C O D$ (SAS rule)

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State true or false:

In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If

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In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If AO=2CO and BO=2DO; Then,ΔAOB is similar to ΔCOD

The correct option is A TrueGiven: AO=2CO or AOCO=2Also given, BO=2DO or BODO=2In △AOB and △COD, we know ∠AOB=∠CODAOCO=BODOThus, △AOB∼△COD (SAS rule)

In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If $A O = 2 C O$ and $B O = 2 D O$ ; Then,
$Δ A O B$ is similar to $Δ C O D$

The correct option is A True
Given: $A O = 2 C O$ or $\frac{A O}{C O} = 2$
Also given, $B O = 2 D O$ or $\frac{B O}{D O} = 2$
In $△ A O B$ and $△ C O D$ , we know
$∠ A O B = ∠ C O D$
$\frac{A O}{C O} = \frac{B O}{D O}$
Thus, $△ A O B \sim △ C O D$ (SAS rule)