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) AB and XY bisect each other at P.
Long Answer TypeShort Answer TypeIn figure given below, AD is the median of ∆ABC.
BE ⊥ AD, CF ⊥ AD. Prove that BE = CF.
Given: AD is the median of ∆ABC. BE ⊥ AD, CF ⊥ AD.
To Prove: BE = CF
Proof: In ∆DEB and ∆DFC,
DB = DC
| ∵ AD is the median of ∆ABC
∠DEB = ∠DFC | Each = 90°
∠BDE = ∠CDF
| Vertically opposite angles
∴ ∆DEB ≅ ∆DFC
| AAS congruence rule
∴ BE = CF | CPCT
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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