Short Answer Type
(i) ∆ABD ≅ ∆BAC
(ii) BD = AC
(iii) ∠ABD = ∠BAC.
Given: I and m are two parallel lines intersected by another pair of parallel lines p and q.
To Prove: ∆ABC ≅ ∆CDA.
Proof: ∵ AB || DC
and    AD || BC
∴ Quadrilateral ABCD is a parallelogram.
| ∵ A quadrilateral is a parallelogram if both the pairs of opposite sides are parallel
∴ BC = AD    ...(1)
| Opposite sides of a ||gm are equal
AB = CD Â Â Â ...(2)
| Opposite sides of a ||gm are equal
and ∠ABC = ∠CDA    ...(3)
| Opposite angles of a ||gm are equal
In ∆ABC and ∆CDA,
AB = CD Â Â Â | From (2)
BC = DA Â Â Â | From (1)
∠ABC = ∠CDA    | From (3)
∴ ∆ABC ≅ ∆CDA.    | SAS Rule
Line I is the bisector of an angle ∠A and B is any point on I. BP and BQ are perpendiculars from B to the arms of ∠A (see figure). Show that:
(i) ∆APB ≅ ∆AQB
(ii) BP = BQ or B is equidistant from the arms of ∠A.
(i) ∆DAP ≅ ∆EBP
(ii) AD = BE.
Long Answer Type
(i)    ∆AMC ≅ ∆BMD
(ii)    ∠DBC is a right angle
(iii)    ∆DBC ≅ ∆ACB
Short Answer Type
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