Geometry and measures worksheet — GCSE Higher

1.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

2.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

3.OABC is a parallelogram, with OA = a and OC = c. M is the midpoint of AB. Express the vector MC in terms of a and c.

4.Triangle D has vertices (3, 1), (3, 5) and (6, 1). It is reflected in the line x = 3. Write down the number of vertices of the triangle that are invariant under this reflection.

5.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.

6.A regular nonagon has 9 sides. Work out the sum of its interior angles.

7.A shape is reflected in the line y = x, and the image is then reflected in the line y = 0. These two lines meet at the origin. Work out the single rotation, centre and angle, that is equivalent to this combination of two reflections, for every point.

8.Point P(2, 5) is enlarged with centre (2, 1) to give image point P′(2, −7). Work out the scale factor of the enlargement.

9.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

10.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

11.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

12.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?

13.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

14.Triangle T has an area of 6 cm². It is enlarged by scale factor −2 about the origin, and the image is then rotated 90° about the origin. Work out the area of the final image, and state whether it is the same way round as T or a mirror image of it.

15.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?