Geometry and measures worksheet — GCSE Foundation

1.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?

2.Write down the term for the distance all the way around the edge of a circle.

3.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.

4.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

5.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

6.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

7.A hiker walks due west. What is the three-figure bearing for this direction?

8.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

9.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

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

12.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

13.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

14.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

15.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?