- Two pairs of equal sides - One pair of equal angles - The diagonals bisect at right angles

- Four sides of equal length - Two pairs of equal angles - Opposite sides are parallel - The diagonals bisect each other at right angles

Geometry and trigonemtry Flashcards by Ben Catchpole

Kite

Two pairs of equal sides
One pair of equal angles
The diagonals bisect at right angles

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Rhombus

Four sides of equal length
Two pairs of equal angles
Opposite sides are parallel
The diagonals bisect each other at right angles

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Radius

The distance from the edge to the centre of a circle

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Chord

A straight line joining two points on the circumference of a circle

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Diameter

The distance from one side of a circle to the other through the centre

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Circumference

The distance around the circle/The perimeter of a circle

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Tangent

A straight line which touches the edge of a circle once

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Arc

A part of the circumference of a circle

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Sector

An area enclosed by two radii and an arc

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Segment

An area enclosed by a chord and an arc

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Quadrilateral

A 2D shape with four sides

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Equilateral triangle

3 sides of equal length and 3 equal angles

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Right-angled triangle

A triangle that has a right angle

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Isosceles triangle

2 sides of equal length and the angles at the base of the equal sides are equal

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Cyclic quadrilateral

A quadrilateral drawn inside a circle where every corner of the quadrilateral touches the circumference of the circle

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Sum of the interior angles of a polygon

180*(n-2)

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The exterior angles of a regular polygon

360/n

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The interior angles of a regular polygon

(180*(n-2))/n

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a²+b²

c²

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sin

opposite/hypotenuse

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cos

adjacent/hypotenuse

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tan

opposite/adjacent

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sin(0)

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cos(0)

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tan(0)

sin(30)

1/2

cos(30)

root(3)/2

tan(30)

root(3)/3

sin(45)

root(2)/2

cos(45)

root(2)/2

tan(45)

sin(60)

root(3)/2

cos(60)

1/2

tan(60)

root(3)

sin(90)

cos(90)

tan(90)

Undefined

Area of a triangle

(1/2)*a*b*sin(C)

Area of a parallelogram

base*height

Area of a trapezium

(1/2)*(a+b)*h

Arc length

(angle/360)*2πr

Sector area

(angle/360)*πr²

Face

A flat surface

Edge

Where two faces meet

Vertex

A corner where edges meet

Volume of a cuboid

length*width*height

Volume of a prism

area of the cross-section*length

Volume of a cylinder

πr²*h

Surface area of a cylinder

2πr²+2πrh

Volume of a cone

(1/3)*πr²*h

Surface area of a cone

πr²+πrh

Volume of a sphere

(4/3)*πr³

Surface area of a sphere

4πr²

1000cm³

Length scale factor

Area scale factor

k²

Volume scale factor

k³

How do you know if two figures are similar?

Their angles are equal and their sides are in proportion

How do you prove two triangles are similar?

- Side Side Side (SSS) - Angle Angle (AA) - Side Angle Side (SAS)

What is the sine rule?

a/sin(A) = b/sin(B) = c/sin(C)

What is the cosine rule?

a² = b²+c²-2bc*cos(A)

d/t

How do you draw a SSS triangle?

1. Draw the longest side as a horizontal line 2. Open your compass so that the radius is the length of one to the remaining sides 3. Draw an arc with centre at one end of the line above it 4. Repeat steps 2 and 3 for the other side 5. Use a ruler to connect the ends of the line to the point of intersection of the arcs

How do you construct the perpendicular bisector of a line?

1. Set the radius of the compass to be more than half the length of the line 2. Place the compass on one end of the line and sketch an arc on either side 3. Repeat this for the other end of the line 4. Connect the points of intersection of the arcs

How do you construct the perpendicular of a line passing through a point?

1. Set the radius of the compass to be greater than the distance between the point and the line 2. Place the compass point on the point and draw two arcs intersecting the line 3. Set the radius of the compass to be more than half the distance between the two points of intersection of the line and the arcs 4. From each point of intersection draw an arc on the opposite side of the line to the point 5. Connect the point where the arcs intersect to the point

How do you construct an angle bisector?

1. Set the radius of the compass to roughly half the distance of the smallest line 2. Sketch an arc intersecting each line with a centre at the point of intersection 3. From each of the points of intersection of the arcs and lines draw an arc 4. Connect the point of intersection of the arcs and the point of intersection of the lines