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Geometry & Trigonometry Guide

1. The document discusses important concepts regarding triangles, including properties of sides and medians, ratios of sides for different angle types, and properties of similar triangles. 2. Key concepts about quadrilaterals, circles, and polygons are also covered, such as formulas for regular polygon areas and angles, properties of secants and tangents of circles, and relationships between chords. 3. Formulas for volumes and surface areas of common 3D shapes like cubes, cuboids, cylinders, cones, spheres and hemispheres are provided in a table.

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Karthikeyan ramamoorthy
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111 views2 pages

Geometry & Trigonometry Guide

1. The document discusses important concepts regarding triangles, including properties of sides and medians, ratios of sides for different angle types, and properties of similar triangles. 2. Key concepts about quadrilaterals, circles, and polygons are also covered, such as formulas for regular polygon areas and angles, properties of secants and tangents of circles, and relationships between chords. 3. Formulas for volumes and surface areas of common 3D shapes like cubes, cuboids, cylinders, cones, spheres and hemispheres are provided in a table.

Uploaded by

Karthikeyan ramamoorthy
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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GE0METRY, MENSURATION AND TRIGONOMETRY

Important points about triangles:

1. Sum of any 2 sides of a triangle is greater than the 3rd side and the difference of any 2
sides of a triangle is less than the 3rd side.

2. To find the lengths of the medians, we can use the Apollonius theorem.
ie If AD is a median to BC
then AB2 + AC2 = 2 (AD2 + BD2)

3. In any triangle the ratio of the sum of the squares of the sides to the sum of the
squares of the medians is 4: 3.

4. In a triangle if the angles are 300,600, 900 ie 1: 2: 3 ratio then the corresponding sides
will be in the ratio 1: √3 : 2.

5. Right angle triangle: AC2 = AB2 + BC2 (if AC is hypotenuse)


Acute angled triangle: AC2 < AB2 + BC2
Obtuse angled triangle: AC2> AB2 + BC2

Similar Triangles:

1. In two similar triangles

a. Ratio of corresponding sides = Ratio of heights = Ratio of medians = Ratio of


perimeters = Ratio of inradii = Ratio of circular radii = Ratio of the lengths of the angular
bisectors.

b. Ratio of areas = Ratio of squares of corresponding sides.

Note:

1. ABC is a right angled triangle, right angled at B. If BD is a median to AC then BD = AD =


DC

2. ABC is right angled triangle, right angled at B. If BD is an altitude to AC then the 2


small triangles ABD and BDC are similar and each inturn is similar to the original
triangle ABC.

Quadrilaterals, Circles, Arcs and Sectors:

a2 π
1. The area of an ‘n’ sided regular polygon = n. cot (n), where a is length of each side.
4

2. If a, b, c, d are the consecutive sides of a cyclic quadrilateral and d1, d2 are its
diagonals then
ac + bd = d1d2
3. The sum of all interior angles of an ’n’ sided regular polygon = (2n – 4)900 and each
(2n−4)900
interior angle = n

360
4. The sum of all exterior angles = 3600 and each exterior angle = n

n(n−3)
5. The no of diagonals of an n sided polygon = 2
6. In a circle PAB, PCD are 2 secant lines, and PT is a tangent then PA × PB = PC × PD =
PT2

7. In a circle, if AB and CD are 2 chords and they intersect at K then AK . KB = CK . KD

θ
8. Length of the arc =360 x 2Пr, where 𝜃 is the central angle and r is the radius of the
circle.

θ
9. Area of the sector =360 x Пr2

Volumes & Surface Areas of Solids:

Sl.No Solid Volume L.S.A T.S.A


1 Cube a 3
4a 2
6a 2

2 Cuboid lbh 2(l+b)xh 2(lb+bh+hl)


3 Cylinder Пr2h 2Пrh 2Пrh+ 2Пr2
1
4 Cone Пr2h Пrl Пrl+Пr2
3
4
5 Sphere Пr3 --------- 4Пr2
3
2
6 Hemisphere Пr3 2Пr2 3Пr2
3

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