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112 The next questions involve the properties of triangles and quadrilaterals. (1) In AABC. EF BC, BA is produced to D. Calculate a and hence show that AE=AF. m (b) (0) (1) (2) Calculate, with reasons, the value of b, c. d and e. In AABC, ED BC. Calculate: (1) the value of x. (2) Calculate the size of D.. (1) ABCD is a parallelogram with AEL BC. Calculate, with reasons, the value of a, b, c and d. ABCD is a parallelogram with B, -90° and À = 70°. (1) Calculate, with reasons, the size of D₁, D₂, B, and B,. (2) Prove that BECD is a parallelogram. (3) Prove that BCED is a rectangle. ABCD is a trapezium with AD BC. AD=BD, BCCD and À = 78. Determine the unknown angles. (k) PQRS is a parallelogram. Calculate the value of x and y. ABCD is a rectangle and DECF is a parallelogram. AFD-90° and AF =DF. Calculate the size of E. Show that EDDC. Show that = ₁. (1) (2) (3) 179 D Sa-40 b 2x+40 A x+10° 70% bAd B E B 70 E (78° 2x+50° 110 S 2a 809 75 B
(m) In the diagram, BC||GK, Ê, = 60°, Es=30°, GE bisects HÊF and BE = BD. (1) (2) (3) (4) (5) Show that BE 1 GK. Show that ABED is equilateral. Show that EF||DB. Calculate the size of C. Show that BD = DC. (n) In ADEF, GH||EF and DGKH is a kite. G₂-40°, Ê= 50°, K₁=x and D = y. (1) (2) Calculate, with reasons, the value of x and y. Show that GK L DE. H G F 4 50⁰ 50° 5 30° 2 40° -K