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1. Angle Sum Property:

The sum of all angles of a triangle is 1800

If a transversal intersects two parallel lines then each

pair of alternate angles are equal. If a transversal intersects two lines such that a pair of

alternate interior angles is equal then the two lines

are parallel.

If a transversal intersect two parallel lines then each

pair of interior angles on the same side of the

transversal is supplementary.

If a transversal intersect two lines such that a pair ofinterior angles on the same side of the transversal is

supplementary then the two lines are parallel.

If a side of an angle is produced then the exterior

angle so formed is equal to the sum of two interior

opposite angles.

1. Area of triangle =ss-as-bs-c

Where s=a+b+c/2

2.Surface Area and Volumes

Cuboid:

Surface Area of Cuboid=2(lb+bh+lh)

Lateral Surface Area=2(l+b)*h

Volume =l*b*h

Cube:

Surface Area=6a2

Curved SurfaceArea=4a2

Volume =a3

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Cylinder:

Total Surface Area=2r(r+h)

Curved Surface Area = 2rhVolume = r2h

Cone:

Total Surface Area=r (L+r)

Curved Surface Area = rL where L= h2+r2

Volume =1/3 r2 h

Hemisphere:

Curved Surface Area =2r2

Total Surface Area= 3r2

Volume= 2/3r3

Sphere:

Surface Area=4r2

Volume=4/3 r3ou

Trigonometry Formulaes:

sin-=-sin cos-=-cos tan-=-

tan

cosec-=-cosec sec-=sec cot-=-cot

sin(90-)=cos cos90-=sin tan90-=cot

cosec90-=sec sec90-=cosec cot90-=tan

sin(90+)=cos cos(90+)=-sin tan(90+)=-cot

cot(90+)=-tan sec(90+)=-cosec cosec(90+)=sec

sin(180-)=sin sec(180-)=-

sec

sin(180+)=-sin

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sec(180+)=-sec cos180-=-cos cosec180-=cosec

cos180+=-cos cosec180+=-cosec tan(180-)=-tan

cot(180-)=-cot tan(180+)=tan cot(180+)=cot

Trigonometrical Ratios of compound angles:

sinA+B=sinAcosB+cosAsinB

cos(A+B)=cosAcosB-sinAsinB

tanA+B=sinA+Bcos(A+B)=sinAcosB+cosAsinBcosAcosB-sinAsinB=tanA+tanB1-

tanAtanB(dividing N & D by cosAcosB)

sinA-B=sinAcosB-cosAsinB

cos(A-B)=cosAcosB+sinAsinB

tanA-B=sinA-Bcos(A-B)=sinAcosB-cosAsinBcosAcosB+sinAsinB=tanA-

tanB1+tanAtanB(dividing N & D by cosAcosB)

cotAB=cotAcotB1cotBcotA

Formulaes for changing the sum or difference into product:

sinsin=2sin/2cos12

cos+cos=2cos12+cos12-

sin2A=2sinAcosA sinA=2sin (A2)cos (A2)

cos2A=cos2A-sin2A,

=1-2sin2A,

=2cos2A-1

cosA=cos2(A2)-sin2(A2)=1-2sin2(A2),

=2cos2(A2)-1

tan2A=2tanA1-tan2A tanA=2tanA2/1-tan2A2

sin3A=3sinA-4sin3A

cos3A=4cos3A-3cosA

tan3A=3tanA-tan3A1-3tan2A

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sin2A=1-cos2A2 sin2(A2)=1-cosA2

cos2A=1+cos2A/2 cos2A2=(1+cosA)/2

tan2A=1-cos2A1+cos2A tan2(A2)=1-cosA1+cosA