# Geometry 10th Standard [इयत्ता १० वी] SSC (Marathi Semi-English) Maharashtra State Board Topics and Syllabus

## Syllabus

100 Similarity
• Properties of ratios of areas of two triangles
• Basic proportionality theorem
• Introduction to similarity
• Similar triangles
• Areas of two similar triangles
• Similarity in right angled triangles
• Pythagoras theorem and its converse
• 30o-60o-90o theorem and 45o-45o-90o theorem
• Application of Pythagoras theorem in acute and obtuse angle.
• Appolonius theorem
300 Circle
• Tangents and its properties
• Theorem - Tangent at any point to the circle is perpendicular to the radius and its converse
• Number of tangents from a point to a circle
• Theorem- The length of two tangent segments drawn from a point outside the circle are equal
• Touching circles
• Introduction to an arc
• Angle subtended by the arc to the centre and to the point on the circle
• Tangent - Secant theorem
400 Co-ordinate Geometry
• Slope of a line
• Intercepts made by a line
• Standard forms of equation of a line
• General equation of a line
500 Geometric Constructions
• Division of line segment in a given ratio
• Basic geometric constructions
• Construction of tangent to the circle from the point on the circle and out side the circle.
• Construction of tangent without using centre
• Construction of triangle If the base, angle apposite to it and either median altitude is given
• Construction of a triangle similar to a given triangle
600 Trigonometry
• Angles in standard position
• Trigonometric ratios in terms of coordinates of point
• Trigonometric Identities (with proof)
• Use of basic identities and their applications
• Problems on height and distance
700 Mensuration
• Length of an arc
• Area of the sector
• Area of a Circular Segment
• Euler's formula
• Surface area and volume of cuboids Spheres, hemispheres, right circular cylinders cones, frustum of a cone
• Problems based on areas and perimeter/circumference of circle, sector and segment of a circle
• Problems on finding surface areas and volumes of combinations of any two of the following :- cuboids, spheres, hemispheres and right circular cylinders/ cones
• Problems involving converting one type of metallic solid into another.