Geometry and measures worksheet — GCSE Foundation

1.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.

2.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

4.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.

5.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

6.Which of the following correctly describes what it means for two lines to be perpendicular?

7.A flower bed in the shape of a parallelogram has a base of 3.5 m and a perpendicular height of 2 m. Compost costs £4.80 per m². Work out the total cost of covering the flower bed with compost.

8.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

9.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

10.A polygon has 9 sides. What is the name of this polygon?

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 tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

13.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

14.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

15.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.