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# Geometry

Geometry mainly deals with shapes. In basic geometry the preliminary concepts line point, line, planes, angles, parallel and perpendicular some basic shapes are covered.

Real life application of geometry is widely seen in computing perimeter, area of places, distances, volumes of 3 dimensional  figures (containers ,swimming pools etc).

Main Topics and Subtopics in Geometry:

1. Basic Geometry

Point
Line, line segment
Ray
Planes
Angles :
Types  of angles  (Acute, obtuse,right)
Angles in Polygons
Angles in parallel lines (cut by transversal)

2. Introduction to basic shapes and their properties (Polygons)

Names of different shapes  based on number of sides
Regular and irregular polygons
Angles in a polygon
3.Triangles

Types of triangles :Triangles are classified based on the angles and sides. Types of  triangles based on angles are acute triangle, right triangle and obtuse triangle.

Types of triangles based on the sides are equilateral triangles, isosceles triangle and scalene triangle.

Properties of triangle

Altitude, median of triangle

Similar triangles  (Proofs )

Congruent Triangles

Types of quadrilaterals based on the sides  and angles .
Square  (all sides and angles are equal).
Rectangle (all angles are right angles and opposite sides are equal)
Parallelogram(Opposite sides and opposite angles are equal)
Trapezoid (One pair of opposite  sides is parallel)
Rhombus
Kite

5.Circles :  different parts of circle like radius, diameter, chord, secant, tangent, arc.

In advanced level  , properties of secant and tangents .intercepted arc, intersection of two circles, apothem will be discussed.

6.Similar and Congruent figures

Proofs related to similar figures.
Properties of similar figures.
Proofs for Congruent figures
Theorems  related to congruent triangles.

7. Perimeter and circumference: Perimeter of basic shapes and composite shapes  and circumference of circle

Real life application of concept in  word problems

8. Area  : Formula for areas for basic shapes  and circles

Area of composite shapes
Area of regular Polygon
Area of irregular polygons

9. 3-D objects Prisms ,Cylinders, Cube, Cone ,Spheres

Introduction to Pyramids . Prisms  ,cylinders and cone
Number of vertices, edges and face of  3-D shapes
Surface area ,lateral surface area
Total surface area of a prism = (perimeter of  base)Xheight + 2area of base
Total surface area of Prism = $\frac{1}{2}$ (perimeter of  base) X height + area of base
Lateral surface area of Prism= perimeter of base X height
Lateral surface area of Pyramid =  $\frac{1}{2}$  perimeter of base X slant height

Volume of a 3 D object

Volume of prisms = Area of base X height
Volume of pyramids = $\frac{1}{3}$ Area of base X height
Volume of sphere = $\frac{4}{3}$ $\pi r^2$
Volume of composite figures  (Ex : Cylinder topped with hemisphere)

10. Pythagorean Theorem in right triangles

Proof
Special right triangles
Application of Pythagorean theorem  to solve right triangles.

Examples:

1. Identify the acute angle from given angles.

Solution:

2.  Find the area of a Circle with radius  of 10 cm. Take $\pi$ = 3.14. Round up the answer to nearest tenth.

Solution: Area of a circle= p$r^2$

= 3.14$(10)^2$

= 314 sq cm.

 Related Calculators Calculate Geometry

 More topics in  Geometry Geometry Problems Plane Geometry Solid Geometry Transformation Symmetry Tangent Secant Theorem Geometric Mean Theorem of Chord Pythagorean Inequality Theorem Types of Angle Pairs
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