Geometry and measures worksheet — GCSE Foundation

1.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

2.A polygon has 9 sides. What is the name of this polygon?

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

4.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

5.Work out the length of the straight line segment joining the points (2, −4) and (−3, −4).

6.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

7.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.

8.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

9.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

10.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

11.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

12.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

13.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

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

15.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.