Geometry and measures worksheet — GCSE Foundation

1.Two triangles are congruent to each other. What does this tell you about their angles and sides?

2.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

3.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.

4.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?

5.Work out the exact value of cos 0° − sin 30°.

6.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

8.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

9.How many edges does a triangular prism have?

10.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

12.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.

13.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

14.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

15.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?