# Question 5

5.1 Use the diagram below to prove that the opposite sides of a parallelogram are equal,
i.e. AB = CD and AD = BC.

Hint: Prove that ∆ ABD = ∆ CDB

(4)

5.2 In the diagram below, KLMN is a parallelogram with N̂ = 7x – 30° and L̂ = 5x + 18°.

5.2.1 Calculate the value of x. (4)

5.2.2 If it is further given that LK̂N = 4y, determine the value of y. (3)

5.3 In the diagram below, ABCD is a parallelogram such that AD = BE, Â = 124°,
ED bisects BÊF and BEFD is a quadrilateral.

Calculate, with reasons, the values of x and y.

(6)

5.4 In the diagram below, FT = 5 cm, ET = 7 cm, EF = 9 cm, CT = 10 cm, DT = 14 cm
and CD = 18 cm.

5.4.1 Prove that ∆ EFT ||| ∆ DCT. (3)

5.4.2 If it is further given that DF̂C = TD̂C, prove that FÊC = TF̂C. (3)

5.5 5.5.1 Complete the following statement for ∆ ABC:

If D is a point on AB and E is a point on AC such that AD = DB and
DE || BC , then … (1)

5.5.2 In ∆ DEF, DS = SE , EU = UF and ST || EF.

Prove that SEUT is a parallelogram. (4)

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