Geometry and measures worksheet — GCSE Higher

1.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

2.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.

3.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

4.O is the centre of a circle, and PT is a tangent to the circle at the point T. A is a point on the circle, with OA and OT both radii and angle AOT = 122°. At the point T, the chord TA lies between the radius TO and the tangent TP. Work out the size of angle ATP, the angle between the chord and the tangent.

5.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

6.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

7.A designer plots a logo point at (3, 4) on a grid. She reflects it in the line y = 1 and then rotates the image 90° clockwise about the point (1, 1) to create a repeating tile pattern. Work out the coordinates of the point after both transformations.

8.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

9.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

10.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?

11.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

12.A garden is made of two triangular flower beds, ABC and ACD, joined along the edge AC. In triangle ABC, angle ABC = 90°, AB = 5 m and BC = 12 m. In triangle ACD, AD = 9 m and angle CAD = 40°, the angle between AC and AD. Work out the area of flower bed ACD. Give your answer to 1 decimal place.

13.A triangular flower bed ABC has AB = 14 m, BC = 9 m and AC = 11 m. Work out the area of the flower bed. Give your answer to 1 decimal place.

14.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

15.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?