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2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig.). Prove that

3. AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB.

5. Line *l *is the bisector of an angle ∠A and B is any point on *l*. BP and BQ are perpendiculars from B to the arms of ∠A (see Fig.). Show that:

(i) ΔAPB ≅ ΔAQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

6. In Fig., AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.