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l\ a n d\ m are two parallel lines in...

`l\ a n d\ m` are two parallel lines intersected by another pair of parallel lines `p\ a n d\ q` as shown in figure. Show that ` A B C~= C D A`

Text Solution

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Please refer to video for the figure.
As line `l` and `m` are parallel and `AC` is their transversal, opposite interior angles will be equal.
So, `/_CAD = /_BCA`
Similarly, as As line `p` and `q` are parallel and `AC` is their transversal, opposite interior angles will be equal.
So, `/_ACD = /_BAC`
Now, in `Delta ABC and Delta CDA`
`/_BCA = /_CAD `
` /_BAC = /_ACD `
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