Short Answer Type
AB is a line-segment. AX and BY are two equal line-segments drawn on opposite sides of line AB such that AX || BY. If AB and XY intersect each other at P. Prove that:
(i)    ∆APX ≅ ∆BPY
(ii) Â Â Â AB and XY bisect each other at P.
Long Answer TypeShort Answer Type
Given: In figure,
∠B = ∠E, BD = CE
and    ∠1 = ∠2
To Prove: ∆ABC ≅ ∆AED
Proof: ∠1 = ∠2
⇒ ∠1 + ∠DAC = ∠2 + ∠DAC
⇒ ∠BAC = ∠EAD    ...(1)
BD = CE
⇒ BD + DC = CE + DC
⇒    BC = ED    ...(2)
∠B = ∠E    ...(3)
In view of (1), (2) and (3),
∆ABC ≅ ∆AED
| AAS congruence rule
In figure given below, AD is the median of ∆ABC.
BE ⊥ AD, CF ⊥ AD. Prove that BE = CF.
Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see figure). Show that: (i) ∆AOB ≅ ∆DOC (ii) O is also the mid-point of BC.
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