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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. 110°. 250°. Base angles in a kite are equal. Opposite angles in a rhombus are equal. - PowerPoint PPT Presentation
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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
110°
Base angles in a kite are equal
Opposite angles in a rhombus are equal
250°
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 5.2P = 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)
9cm
5cm 5cm
5cm
3cm 3cm Can choose either as your answer
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
Isosceles TriangleAngles in a triangle
add to 180°
180° - 34° = 146° 146° ÷ 2 = 73°
73
73°
73°
107°
107° because angles on a straight line add up to 180°
y = 180° - 107° - 38° = 35°
35
35°
No, because 38° is not equal to 35°. Therefore, it is not an isosceles triangle
180° - 126° = 54° 54° ÷ 2 = 27°
27° 27° 153°
153° because angles on a straight line add up to 180°
Angles in a triangle add to 180°
27 153
Base angles are the same in an isosceles triangle
80°
Angles in a triangle add to 180°180° - 80° - 80° = 20°
20
Means work out angle A in triangle ABC
Means work out angle R in triangle PQR
Base angles are the same in an isosceles triangle
70°
Angles in a triangle add to 180°180° - 70° - 70° = 40°
40°
A right angle is 90°90° - 40° = 50°
50°
Both base angles are equal180° - 50° = 130° 130° ÷ 2 = 65°
65°65°
65
180° - 48° = 132° 132° ÷ 2 = 66°
66° 66°
Angles on a straight line add to 180°180° - 66° = 114°
114°
114
A quadrilateral is made up of two triangles Angles is a triangle add up to 180°
180°
180° 180° + 180° = 360°
LEARN OFF BY HEART
(because the exterior angles add up to 360°)
Exterior angle = 72°
72°
Two exterior angles joined
togetherAs worked out in part (a)
72°
144
All the angles and sides are the same in a regular pentagon
LEARN OFF BY HEART
Exterior angle
Exterior angle
Exterior angle
Exterior angle
Exterior angle
= 72°
72°
72°
72°
72°
72°
Interior angle
Angles on a straight line add up 180° Interior angle = 180° - 72° = 108°
108°
Base angles in a isosceles triangle are the same 180° - 108° = 72°
36°
36°
36
LEARN OFF BY HEARTInterior angle
Exterior angle
Angles on a straight line add up 180°
Exterior angle = 180° - 162° = 18°
= 20 20
Decagon Pentagon
Interior angle
Sum of interior angles of an decagon = (10 – 2) x 180°
Sum of interior angles = (number of sides – 2) x 180°
LEARN OFF BY HEART
= 8 x 180° = 1440°
= 144°
144°Interior angle
Sum of interior angles of a pentagon = (5 – 2) x 180° = 3 x 180° = 540°
= 108°
108°
Angles around a point add up to 360°
360° - 144° - 108° = 108°
108°
Base angles in a isosceles triangle are the same
180° - 108° = 72° 72° ÷ 2 = 36°
36°36°
144°
144° + 36° = 180° (Angles on a straight line add up to 180°) Therefore, ABC lie on a straight line
Hexagon
Square
Square
Sum of interior angles = (number of sides – 2) x 180°
LEARN OFF BY HEART
Sum of interior angles of an hexagon = (6 – 2) x 180° = 4 x 180° = 720°
= 120°
Interior angle120°
Angles around a point add up to 360°
360° - 120° - 90° - 90° = 60°
60°
Base angles are the same
180° - 60° = 120° 120° ÷ 2 = 60°
60°60°
Therefore, as all angles are 60° AHJ is equilateral
Sum of interior angles = (number of sides – 2) x 180°
LEARN OFF BY HEARTSum of interior angles of an octagon = (8 – 2) x 180° = 6 x 180° = 1080°
= 135°
135
= 135° As worked out in part (a)
135°
135°135°
135° 135°135°
135°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
40°
Angles on a straight line add up 180°180° - 110° = 70°
70°
Angles in a triangle add up 180°
180° - 40° - 70° = 70°
70°
As both base angles are 70°, triangle BEF is isosceles.
55°
Alternate angles are equal
Angles in a triangle add up 180°
180° - 70° - 55° = 55°
55°
As both base angles are 55°, triangle ABC is isosceles.
41°
41
Interior angles add up to 180°
180° - 67° = 113°
113°
113
2
Perimeter of rectangle A =
Perimeter is the length around a
shape
14cmPerimeter of rectangle B =
16cm Difference = 16cm - 14cm2
OTHER ANSWERS
ALSO ALLOWED
4cm
4cm
3cm3cm
6cm
2cm
6cm
2cm
6cm
6cm
4cm4cmPerimeter is the length around a
shape
Perimeter of rectangle = 6cm + 4cm + 6cm + 4cm
20
Square has 4 equal sides
3cm for each side
x
x
x
xOTHER
ANSWERS ALSO
ALLOWED
Because two lengths of 12cm makes 24cm which is more than the perimeter
As evident from the rectangle drawn for part (a)
40cm
1cm
40cm
1cm
20cm
2cm
20cm
2cm
10cm
4cm
10cm
4cm
8cm
5cm
8cm
5cm
Find the only rectangle which has a perimeter
of 26cm
85
Kilo means a thousand
1km = 1000m
1000m
Area = Length x Width
= 1000m x 10m
Split compound shape into two rectangles
Rect
angl
e A
Rectangle B
200m
Area of rectangle A = 100 x 30
Area of rectangle B = 200 x a 200a + 3000 = 10000
200a = 7000 35
Count the number of squares to find the area
C B E
Shaded Area = Area of square – Area of circle
Area of square = length x width= 80cm x 80cm
Area of circle = = 3.14 x 30cm x 30cm
Area shaded = 6400 - 28263574
LEARN THE FORMULAE OFF BY HEART
Diam
eter30
cm
equal to (because the length around the shape is the same)
less than (because more than half the rectangle is unshaded)
Shaded Area = Area of big square ABCD – Area of the 4 congruent (identical) triangles
10cm
10cm
Area of big square = length x width= 10cm x 10cm
Area of one triangle = Area of one triangle = Area of one triangle = Area of four triangles =
Shaded area =
82
Area of small square = 30cm x 30cm
900
Length of large square = 50
Area of floor = 300cm x 180cmNumber of small tiles needed = Number of small tiles needed =
60
2cm2cm
2cm2cm
Perimeter is the length around a
shape
Perimeter of D = 2cm + 2cm + 2cm + 2cm
8
Perimeter A = 10cmPerimeter B = 9cm
Perimeter C = 10cm
A and C
Area is the space inside a shapeC and D
Shaded Area = Area of big square – Area of two smaller squares
Area of big square = 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 widthArea of one small square = length x widthArea of both squares = Shaded Area =
Fraction shaded = Unshaded
6
A, B and E