Topics
Similarity
- Properties of Ratios of Areas of Two Triangles
- Basic Proportionality Theorem
- Property of an Angle Bisector of a Triangle
- Property of Three Parallel Lines and Their Transversals
- Similarity of Triangles (Corresponding Sides & Angles)
- Relation Between the Areas of Two Triangles
- Criteria for Similarity of Triangles
- Overview of Similarity
Pythagoras Theorem
- Pythagoras Theorem
- Pythagorean Triplet
- Property of 30°- 60°- 90° Triangle Theorem
- Property of 45°- 45°- 90° Triangle Theorem
- Similarity in Right Angled Triangles
- Theorem of Geometric Mean
- Right-angled Triangles and Pythagoras Property
- Converse of Pythagoras Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Apollonius Theorem
- Overview of Pythagoras Theorem
Circle
- Circles Passing Through One, Two, Three Points
- Tangent and Secant Properties
- Secant and Tangent
- Inscribed Angle Theorem
- Intersecting Chords and Tangents
- Corollaries of Inscribed Angle Theorem
- Angle Subtended by the Arc to the Point on the Circle
- Angle Subtended by the Arc to the Centre
- Overview of Circle
Geometric Constructions
Co-ordinate Geometry
Trigonometry
- Trigonometric Ratios in Terms of Coordinates of Point
- Angles in Standard Position
- Trigonometric Ratios
- Trigonometry Ratio of Zero Degree and Negative Angles
- Trigonometric Table
- Trigonometric Identities (Square Relations)
- Angles of Elevation and Depression
- Relation Among Trigonometric Ratios
- Trigonometric Ratios of Specific Angles
Mensuration
Maharashtra State Board: Class 10
Key Points: Ratio of Areas of Two Triangles
- Ratio of areas of two triangles is equal to the ratio of the products of their bases and corresponding heights.
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Areas of triangles with equal heights are proportional to their corresponding bases.
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Areas of triangles with equal bases are proportional to their corresponding heights.
Maharashtra State Board: Class 10
Theorem: Angle Bisector Theorem
Statement:
The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
\[\frac{AE}{EB}=\frac{CA}{CB}\]
Maharashtra State Board: Class 10
Theorem: Property of Three Parallel Lines and Their Transversals
Statement:
The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines.
\[\frac{\mathrm{AB}}{\mathrm{BC}}=\frac{\mathrm{PQ}}{\mathrm{QR}}\]
