Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

2.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

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

4.Write down the number of lines of symmetry a rhombus has.

5.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

6.A circle has a radius of 3 cm. Work out the diameter of the circle.

7.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

8.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

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

10.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

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

12.How many vertices does a cylinder have?

13.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

14.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?

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