Geometry and measures worksheet — GCSE Foundation

1.A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. Work out the area of the parallelogram.

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

3.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

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

5.Write down the number of lines of symmetry a rhombus has.

6.Write down the column vector, from the options given, that would move a point to the right and downwards.

7.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?

8.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

9.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

10.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

11.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

12.a is the column vector with top number 3 and bottom number 2. b is the column vector with top number −1 and bottom number 4. Work out a + b, giving your answer as a column vector in the form (top, bottom).

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

14.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

15.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?