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GCSE maths > 5.) Geometry & Measures > Flashcards

5.) Geometry & Measures Flashcards

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1
Q

What do (internal) angles in a triangle and a quadrilateral add up to?

A
  • Angles in a triangle add up to 180°
  • Angles in a quadrilateral add up to 360°
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2
Q

What do alternate, allied and corresponding angles (of parallel lines) look like and what are their rules?

A
  • Alternate angles are equal (Z shape)
  • Allied angles add up to 180° (C or U shape)
  • Corresponding angles are the same (F shape)
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3
Q

What do the sum exterior and interior angles of any polygon make up?

A
  • Sum of exterior angles is always 360°
  • Sum of the interior angles = (number of sides – 2) * 180°
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4
Q

For regular polygons, how do you find each individual interior and exterior angle?

A
  • Exterior angle = 360° ÷ number of sides
  • Interior angle is just 180° - the exterior angle
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5
Q

(Rule of circle geometry) involving the angle of a tangent and radius:

A
  • They always meet at 90°
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6
Q

(Rule of circle geometry) What do 2 radii form?

A
  • An isosceles triangle
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7
Q

(Rule of circle geometry) What is the angle of a point on the circumference drawn out from two ends of a diameter, aka the angle of a semicircle?

A
  • 90°
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8
Q

(Rule of circle geometry) The one about perpendicular bisector and chord? Also what do those two phrases mean?

A
  • The perpendicular bisector of a chord always passes through the centre of a circle
  • A chord is any straight line through a circle
  • A perpendicular bisector cuts a line at 90°
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9
Q

(Rule of circle geometry) How do the angles at the centre and at the circumference relate?

A
  • The angle at the centre of the circle is always the angle at the circumference
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10
Q

(Rule of circle geometry) What can you say about angles in the same segment?

A
  • They are equal
  • (2 angles drawn from the same chord)
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11
Q

(Rule of circle geometry) What can you say about opposite angles in a cyclic quadrilateral? And what is a cyclic quadrilateral

A
  • A cyclic quadrilateral is inside a circle where all four points touch the circumference
  • 2 opposite angles in a cyclic quadrilateral always add up to 180°
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12
Q

(Rule of circle geometry) What can you say about 2 tangents from the same point?

A
  • They are the same length
  • As they are both the hypotenuse of 2 congruent right-angled triangles
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13
Q

(Rule of circle geometry) What is the alternate segment theorem?

A
  • The angle between a tangent & chord is the same as the angle in the opposite segment
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14
Q

Four ways of proving a pair of triangles being congruent?

A
  • SSS: 3 sides are the same length
  • AAS: 2 sides and a corresponding angle match up
  • SAS: 2 sides and the angle in between them match up
  • RHS: The hypotenuse and another side of a right angle match up
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15
Q

Difference between “similar” and congruent?

A
  • Two congruent shapes are the same shape and size
  • Two similar shapes are the same shape but different size
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16
Q

How do you describe a shape’s translation?

A
17
Q

How do you describe a shape’s rotation?

A
  • Give the centre of rotation (most often the origin at GCSE)
  • The angle of rotation
  • Direction (clockwise vs anticlockwise)
18
Q

How do you describe a shape’s reflection?

A
  • Just give the line it rotates on (X axis, Y =X, etc)
19
Q

How do you describe a shape’s enlargement?

A
  • Give the scale factor (how much it grows/shrinks by)
  • Give the centre of enlargement (the point where all the lines of corresponding vertices will meet)
20
Q

Area of a trapezium:

A
  • (Average of parallel sides) * vertical height
21
Q

Area for circumference and area of circle

A
  • Area = πr2
  • Circumference = 2πr
22
Q

Surface area of a sphere (given in exam, but good to learn!)

A
  • 4πr2
23
Q

Surface area of a cone (given in exam, but good to learn!)

A
  • πrl +πr2 (area of the base)
  • l is the slant height
24
Q

Surface area of a cylinder:

A
  • 2πrh + 2πr2
  • Think about it as the two circles on each end with a rectangle in the middle, where the width is the circumference
25
Q

Volume of a sphere (given in exam, but good to learn!)

A
26
Q

Volume of a pyramid and cone

A

GCSE maths (8 decks)

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