Geometry and measures worksheet — GCSE Foundation

1.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

2.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

3.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

4.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

5.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

6.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

7.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).

8.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

9.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

10.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

11.Write down the term for the distance all the way around the edge of a circle.

12.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

13.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

14.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.

15.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?