1. 1
   Triangle ABC has AB = 7 cm, BC = 7 cm and angle ABC = 50°. Quadrilateral PQRS is a parallelogram with PQ = 9 cm and angle PQR = 65°.

   (a)

   What type of triangle is ABC?

   [1 mark]

   • ARight-angled
   • BEquilateral
   • CScalene
   • DIsosceles

   (b)

   What is the size of angle BAC?

   [1 mark]

   • A55°
   • B50°
   • C65°
   • D90°

   (c)

   What is the size of angle QRS in parallelogram PQRS?

   [1 mark]

   • A65°
   • B115°
   • C90°
   • D130°

   Total for question 1: 3 marks

2. 2
   A rhombus WXYZ has all sides equal to 6 cm. One of its interior angles, angle WXY, is 70°.

   (a)

   Find the size of angle XYZ.

   [2 marks]

   (b)

   Find the size of angle YZW.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A regular polygon has 9 sides (a nonagon).

   (a)

   Calculate the sum of the interior angles of this polygon.

   [3 marks]

   (b)

   Calculate the size of one interior angle of the polygon.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Two triangles, PQR and STU, have PQ = 8 cm, QR = 6 cm and angle PQR = 90°, and ST = 8 cm, TU = 6 cm and angle STU = 90°.

   (a)

   Explain, using an appropriate congruence criterion, why triangle PQR is congruent to triangle STU.

   [4 marks]

   (b)

   Given also that PR = 10 cm, use Pythagoras' theorem to confirm this is consistent with a right angle at Q, then state the length of SU.

   [4 marks]

   (c)

   A third triangle VWX has VW = 8 cm, WX = 6 cm and VX = 10 cm. Use the SSS criterion to justify whether triangle VWX must be congruent to triangle PQR, and explain whether angle VWX must equal 90°.

   [5 marks]

   Total for question 4: 13 marks

End of questions