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

Rhombus Trapezium Rectangle Rhombus

Rhombus

Parallelogram Rhombus Trapezium or Right-angle Trapezium

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    

Kite Trapezium

Replace a with 3 and b with 5.2 P = 2 x 3 + 2 x 5.2 P = 6 + 10.4 16.4           Total areas of both shapes are equal to one as shown.

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

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.

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

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

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

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°

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°

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

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

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

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

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

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

      2.5 -1

Alternate angles are equal 70° 40° 70° Alternate angles are equal Angles on a straight line add up 180° 180° - 110° = 70° Angles in a triangle add up 180° 180° - 40° - 70° = 70° As both base angles are 70°, triangle BEF is isosceles.

Alternate angles are equal 55° 55° Alternate angles are equal Angles in a triangle add up 180° 180° - 70° - 55° = 55° As both base angles are 55°, triangle ABC is isosceles.

41° 113° 41 Interior angles add up to 180° 180° - 67° = 113° 113

OTHER ANSWERS ALSO ALLOWED Perimeter is the length around a shape 2 4cm 3cm 3cm OTHER ANSWERS ALSO ALLOWED 4cm 6cm 2cm 2cm 6cm Perimeter of rectangle A = 14cm Perimeter is the length around a shape Perimeter of rectangle B = 16cm Difference = 16cm - 14cm 2

Perimeter is the length around a shape 6cm 4cm 4cm Perimeter is the length around a shape 6cm Perimeter of rectangle = 6cm + 4cm + 6cm + 4cm 20 Square has 4 equal sides   3cm for each side

OTHER ANSWERS ALSO ALLOWED x x x x   Because two lengths of 12cm makes 24cm which is more than the perimeter As evident from the rectangle drawn for part (a)

Find the only rectangle which has a perimeter of 26cm   40cm 1cm 20cm 2cm 10cm 4cm 8cm 5cm Find the only rectangle which has a perimeter of 26cm 8 5

Split compound shape into two rectangles Kilo means a thousand 1km = 1000m 1000m Area = Length x Width = 1000m x 10m     Split compound shape into two rectangles Rectangle A 200m Rectangle B Area of rectangle A = 100 x 30   Area of rectangle B = 200 x a   200a + 3000 = 10000 35 200a = 7000

Count the number of squares to find the area       C B E

Shaded Area = Area of square – Area of circle 30cm Diameter LEARN THE FORMULAE OFF BY HEART Area of square = length x width = 80cm x 80cm   Area of circle =   = 3.14 x 30cm x 30cm   Area shaded = 6400 - 2826 3574

equal to less than (because the length around the shape is the same) (because more than half the rectangle is unshaded)

10cm 10cm Shaded Area = Area of big square ABCD – Area of the 4 congruent (identical) triangles Area of big square = length x width = 10cm x 10cm   Area of one triangle = Area of one triangle = Area of one triangle =   Shaded area =   Area of four triangles =     82

900 50 60 Area of small square = 30cm x 30cm Length of large square =   50 Area of floor = 300cm x 180cm   Number of small tiles needed = Number of small tiles needed = 60

8 A and C C and D Perimeter is the length around a shape Perimeter B = 9cm Perimeter A = 10cm Perimeter is the length around a shape 2cm 2cm 2cm 2cm Perimeter C = 10cm Perimeter of D = 2cm + 2cm + 2cm + 2cm 8 A and C Area is the space inside a shape C and D

Shaded Area = Area of big square – Area of two smaller squares length x width = 12cm x 12cm   Area of one small square = length x width = 4cm x 4cm   Area of both squares =     Shaded Area =     Area of big square = length x width     Area of one small square = length x width     Area of both squares =     Shaded Area =         Fraction shaded =   Unshaded

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A, B and E