In given figure- AO OC - BO OD - 1 2 and AB-5 cm- Find the value of DC-

In AOB and COD , we have #160; ∠ AOB=∠ COD #160; #160; #160; #160;[Vertically opposite angles] #160; #160; AO OC = OB ...

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Byju's Answer

Standard IX

Mathematics

Opposite Sides of a Parallelogram Are Equal

In given figu...

Question

In given figure, $\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}$ and AB=5 cm. Find the value of DC.

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Solution

In $△ A O B$ and $△ C O D$ , we have

$∠ A O B = ∠ C O D$ [Vertically opposite angles]

$\frac{A O}{O C} = \frac{O B}{O D}$ [Given]

So, by SAS-criterion of similarity, we have

$△ A O B \sim △ C O D$

$\Rightarrow$ $\frac{A O}{O C} = \frac{B O}{O D} = \frac{A B}{D C}$

$\Rightarrow$ $\frac{1}{2} = \frac{5}{D C}$ [ $∵$ AB=5 cm]

$\Rightarrow$ $D C = 10 c m$

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In given figure, AOOC=BOOD=12 and AB=5 cm. Find the value of DC.

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In given figure, $\frac{A O}{O C} = \frac{B O}{O D} = \frac{1}{2}$ and AB=5 cm. Find the value of DC.