Maharashtra State BoardSSC (Marathi Semi-English) 9th
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# Geometry 9th SSC (Marathi Semi-English) Maharashtra State Board Topics and Syllabus

SubjectGeometry

## Topics with syllabus and resources

1.00 Basic Concepts in Geometry
2.00 Parallel Line

3.00 Triangles
4.00 Constructions of Triangles
• Perpendicular bisector Theorem
• Perpendicular bisector Theorem
• Construction of Triangles
• To construct a triangle when its base, an angle adjacent to the base and the sum of the lengths of remaining sides is given.

• To construct a triangle when its base, angle adjacent to the base and difference between the remaining sides is given.

• To construct a triangle, if its perimeter, base and the angles which include the base are given.

• Parallelogram
• Opposite sides and opposite angles of a parallelogram are congruent.
• Diagonals of a parallelogram bisect each other.
• If a pair of opposite sides of a quadrilateral are equal and parallel, it is a parallelogram.
• Tests for parallelogram
• If pairs of opposite sides of a quadrilateral are congruent then that quadrilateral is a parallelogram.
• If both the pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram.
• If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
• A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
• Properties of Rhombus
• Diagonals of a rhombus are perpendicular bisectors of each other.
• Properties of Square
• Diagonals of a square are congruent.
• Properties of Rectangle
• Diagonals of a rectangle are congruent.
• The Mid-point Theorem
• Theorem of midpoints of two sides of a triangle : The line segment joining the mid-points of any two sides of a triangle is parallel to the third side, and is equal to half of it.

• Converse of midpoint theroem : The straight line drawn through the mid-point of one side of a triangle parallel to another, bisects the third side.
6.00 Cirle
• Concept of Circles
• Circle
• Centre of the circle
• Chord
• Diameter
• Concentric Circle
• Properties of Chord

Properties of congruent chords:

• A perpendicular drawn from the centre of a circle on its chord bisects the chord.
• The segment joining the centre of a circle and the midpoint of its chord is perpendicular to the chord.

Relation between congruent chords of a circle and their distances from the centre

• Congruent chords of a circle are equidistant from the centre of the circle.

• The chords of a circle equidistant from the centre of a circle are congruent.

• Incircle Of a triangle
• Circumcircle of circle
9.00 Surface area and volume
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