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l and m are two parallel lines intersec...

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that `DeltaA B C~=DeltaC 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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