1. 1
   Triangle ABC has AB = 6 cm, BC = 8 cm and angle ABC = 90°. Triangle DEF has DE = 6 cm, EF = 8 cm and angle DEF = 90°.

   (a)

   Which condition proves that triangle ABC is congruent to triangle DEF?

   [1 mark]

   • AAAA (three angles)
   • BSAS (two sides and the included angle)
   • CSSA (two sides and a non-included angle)
   • DNo congruence can be shown

   (b)

   What is the length of AC?

   [1 mark]

   • A7 cm
   • B14 cm
   • C48 cm
   • D10 cm

   (c)

   Given the congruence in part (a), what is the length of DF?

   [1 mark]

   • A8 cm
   • B6 cm
   • C10 cm
   • D14 cm

   Total for question 1: 3 marks

2. 2
   Triangles PQR and STU are similar, with PQ corresponding to ST and QR corresponding to TU. PQ = 5 cm, QR = 7 cm, ST = 15 cm.

   (a)

   Find the scale factor of enlargement from triangle PQR to triangle STU.

   [2 marks]

   (b)

   Find the length of TU.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle ABC, D is the midpoint of BC. AD is drawn, and it is given that AB = AC.

   (a)

   Prove that triangle ABD is congruent to triangle ACD.

   [3 marks]

   (b)

   Hence prove that AD is perpendicular to BC.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In triangle ABC, points D and E lie on AB and AC respectively, such that DE is parallel to BC. AD = 4 cm, DB = 6 cm, and DE = 8 cm.

   (a)

   Prove that triangle ADE is similar to triangle ABC.

   [4 marks]

   (b)

   Using the similarity from part (a), find the length of BC.

   [4 marks]

   (c)

   Given that the area of triangle ADE is 12 cm², find the area of trapezium DBCE.

   [5 marks]

   Total for question 4: 13 marks

End of questions