Geometry and measures worksheet — GCSE Foundation

1.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

2.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

3.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

4.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

5.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

6.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

7.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

8.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

9.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

10.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

11.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

12.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.

13.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

14.Which of these describes an obtuse angle?

15.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.