Geometry and measures worksheet — GCSE Foundation

1.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

2.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.

3.An angle is measured with a protractor as 47°. What type of angle is this?

4.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

5.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

6.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

7.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.

8.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

9.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

10.Work out the distance between the points (−3, 4) and (5, −2).

11.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

12.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

13.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

14.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

15.Write down how many right angles a right-angled triangle has.