Geometry and measures worksheet — GCSE Foundation

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

2.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

3.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

4.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

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

6.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

7.What does the statement AB = CD mean, where A, B, C and D are all points?

8.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

9.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

10.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

11.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

12.Write down the exact value of tan 60°.

13.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

14.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.