1. EVERYTHING YOU NEED TO KNOW TO GET A GRADE C
GEOMETRY & MEASURES
(FOUNDATION)
AUTHOR

2. Rhombus
Trapezium
Rectangle
Rhombus

3. Rhombus

4. Parallelogram
Rhombus
Trapezium or Right-angle Trapezium

5. 30 Base angles in a kite are equal
Opposite angles in a rhombus are equal
110°
250°
Base angles in a kite are equal
Angles around a point sum to 360°
Angles in a kite sum to 360° 30

6. Kite
Trapezium

7. Replace a with 3 and b with 5.2
P = 2 x x 5.2
P =
16.4
Total areas of both shapes are equal to one as shown.

8. Equilateral triangle Rhombus 2
(Fits on top of itself twice through a full turn)

9. Can choose either as your answer
5cm
5cm
Can choose either as your answer
3cm
3cm
9cm
5cm
Any two of rectangle, parallelogram, kite or arrowhead
The 3cm and 5cm rods would not meet
when joined with the 9cm rod.

10. In an isosceles triangle, the base angles are the same
Angles in a triangle sum to 180° 80 20 50 50
Each angle is 60° in an equilateral triangle
120° because angles on a straight line add to 180°
30° because angles in a right angle add to 90°
Base angles are both 30° so ABD is an isosceles triangle

11. Angles in a triangle add to 180°
Isosceles Triangle
Angles in a triangle add to 180°
35°
73°
107°
73°
107° because angles on a straight line add up to 180°
180° - 34° = 146°
146° ÷ 2 = 73° 73
y = 180° - 107° - 38° = 35° 35
No, because 38° is not equal to 35°. Therefore, it is not an isosceles triangle

12. Angles in a triangle add to 180°
27°
27°
153°
180° - 126° = 54°
54° ÷ 2 = 27°
153° because angles on a straight line add up to 180° 27
153

13. Base angles are the same in an isosceles triangle
80°
Means work out angle A in triangle ABC
Angles in a triangle add to 180°
180° - 80° - 80° = 20° 20
Base angles are the same in an isosceles triangle
65°
65°
70°
50°
40°
Means work out angle R in triangle PQR
Angles in a triangle add to 180°
180° - 70° - 70° = 40°
A right angle is 90°
90° - 40° = 50° 65
Both base angles are equal
180° - 50° = 130°
130° ÷ 2 = 65°

14. Angles on a straight line add to 180°
180° - 48° = 132°
132° ÷ 2 = 66°
Angles on a straight line add to 180°
180° - 66° = 114°
66°
66°
114°
114
A quadrilateral is made up of two triangles
180°
Angles is a triangle add up to 180°
180° + 180° = 360°
180°

15. Two exterior angles joined together
LEARN OFF BY HEART
(because the exterior angles add up to 360°)
Exterior angle = 72°
Two exterior angles joined together
72°
As worked out in part (a)
72°
144

16. All the angles and sides are the same in a regular pentagon
Exterior angle
72°
36°
LEARN OFF BY HEART
Interior angle
108°
36°
= 72°
Angles on a straight line add up 180°
Interior angle = 180° - 72°
= 108°
Base angles in a isosceles triangle are the same
180° - 108°
= 72° 36

17. 20 Interior angle LEARN OFF BY HEART Exterior angle
Angles on a straight line add up 180°
Exterior angle = 180° - 162°
= 18°
= 20 20

18. Sum of interior angles = (number of sides – 2) x 180°
Decagon
Pentagon
LEARN OFF BY HEART
Interior angle
Interior angle
108°
144°
Sum of interior angles = (number of sides – 2) x 180°
108°
36°
144°
36°
Sum of interior angles of an decagon = (10 – 2) x 180°
= 8 x 180°
= 1440°
= 144°
Sum of interior angles of a pentagon = (5 – 2) x 180°
= 3 x 180°
= 540°
= 108°
Angles around a point add up to 360°
360° - 144° - 108°
= 108°
Base angles in a isosceles triangle are the same
180° - 108° = 72°
72° ÷ 2 = 36°
144° + 36°
= 180°
(Angles on a straight line add up to 180°)
Therefore, ABC lie on a straight line

19. Sum of interior angles = (number of sides – 2) x 180°
LEARN OFF BY HEART
Sum of interior angles = (number of sides – 2) x 180°
Hexagon
Interior angle
120°
Square
60°
Square
60°
60°
Sum of interior angles of an hexagon = (6 – 2) x 180°
= 4 x 180°
= 720°
= 120°
Angles around a point add up to 360°
360° - 120° - 90° - 90°
= 60°
Base angles are the same
180° - 60°
= 120°
120° ÷ 2
= 60°
Therefore, as all angles are 60° AHJ is equilateral

20. As worked out in part (a)
LEARN OFF BY HEART
Sum of interior angles of an octagon = (8 – 2) x 180°
= 6 x 180°
= 1080°
= 135°
Sum of interior angles = (number of sides – 2) x 180°
135
135°
135°
135°
As worked out in part (a)
= 135°
Angles around a point add up to 360°
360° - 135° - 135°
= 90°
Therefore, as all angles are 90° PQRS is a square