Question

ab||cd . prove ∆abn ~cod and ab=20,DC =12,ao=25, find co​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• AB//CD
• AB=20
• CD=12
• BO=25

${\sf{\green{\underline{\large{To\:find}}}}}$

• CO?
• ∆ABO ~ ∆COD

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Diagram

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{B}}\put(9.5,0.7){\sf{\large{Base}}}\put(11.1,0.9){\large{C}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(7.7,2){\large{ \sf\:side }}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\put(8,1){\line(2,1){4}}\put(11,1){\line(-1,1){2}}\end{picture}$

Solution

Here

AB//CD

DCO=OAB ((alternate interior)

OBA= BOC (alternate interior)

∆ABN ~ ∆COD (By AA Similarity)

• If two ∆s are similar than their sides are proportional to each other

∆ABN ~ ∆COD

• From this we conclude that

$\tt\rightarrow\dfrac{CO}{BO}=\dfrac{OD}{OA}=\dfrac{CD}{AB}$

¶utting the values

$\tt\rightarrow\dfrac{CO}{BO}=\dfrac{OD}{OA}=\dfrac{CD}{AB}$

$\tt\rightarrow\dfrac{CO}{BO}=\dfrac{CD}{AB}$

$\tt\rightarrow\dfrac{CO}{25}=\dfrac{12}{20}$

=>CO= (12 ×25) / 20

=>CO=15

Answer 2

Step-by-step explanation:

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