Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

2.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

3.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

4.A bus journey takes 2.5 hours. Work out how many minutes this is.

5.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

6.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

7.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

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

9.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

10.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

11.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

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

13.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

14.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

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