Geometry and measures worksheet — GCSE Foundation

1.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

2.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

3.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?

4.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

5.In this question, a curved surface counts as a face. How many faces does a cone have?

6.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.

7.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².

8.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

9.A scale drawing of a bridge uses a scale of 1 : 25. A support beam on the drawing measures 4.4 cm. What is the real length of the beam, in metres?

10.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

11.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

12.Point C is at (2, 3). It is rotated 90° clockwise about the origin. Work out the coordinates of the image of point C.

13.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

14.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

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?