Q12 of 47 Page 7

In the figure, ∠B = ∠C and AB = AC. Prove that BD = CE.

In ΔABD and ΔACE,
    AB = AC ...... (given)
    ∠B = ∠C ...... (given)
    ∠A = ∠A ...... (common)
... ΔABD ≅ ΔACE ...... (By ASA criterion)
  ... BD = CE ...... (c.p.c.t.)

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10 In the figure x is a point in the interior of square ABCD, AXYZ is also a square. Prove that BX = DZ.
 11 In the figure, the sides AB and BC of square ABCD are produced to P and Q respectively so that BP = CQ. Prove that DP and AQ are perpendicular to each other.
 13 In the figure, AD = BE, BC = DF and ∠ABC = ∠EDF. Prove that AC ïï EF and AC = EF.
14 Given ABCD is a parallelogram, BC is produced to F and BD is produced to E and AE=CF Prove that:
(i) BE || DF
(ii) BD and EF bisect each other.