Geometry and measures worksheet — GCSE Foundation

1.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

2.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).

3.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

4.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?

5.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

6.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

7.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

8.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

9.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

10.A vertical line passes through the point (5, 2). Write down the equation of this line.

11.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

12.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.

13.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

14.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

15.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?