Basic Proportionality Theorem (Thales's Theorem) and its Applications | Problems, Online Practice, Tests, Worksheets, Quizzes, Assignments | Class 10 | NCERT (CBSE and ICSE)

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Class 10
Triangles
Basic Proportionality Theorem (Thales's Theorem) and its Applications

Class 10

1. Real Numbers

1.1. Euclid's Division Lemma

1.2. The Fundamental Theorem of Arithmetic

1.3. Revisiting Irrational Numbers

2. Polynomials

2.1. Zeros of a Quadratic Polynomial and Relation Between Its Zeroes and Coefficients

2.2. Zeros of a Cubic Polynomial and Relation Between Its Zeroes and Coefficients

2.3. Division Algorithm for Polynomials

3. Pair of Linear Equations in Two Variables

3.1. Forming Linear Equations Under the Given Conditions

3.2. Solutions of a Linear Equation

3.3. Solving a System of Simultaneous Linear Equations

3.3.1. Solving Simultaneous Linear Equations by Graphical Method

3.3.2. Solving Simultaneous Linear Equations by Algebraic Method

3.3.2.1. Substitution Method

3.3.2.2. Elimination Method

3.3.2.3. Cross Multiplication Method

3.4. Conditions for Solvability of a System of Linear Equations

3.4.1. System of Equations with Unique Solution

3.4.2. System of Equations with Infinitely Many Solutions

3.4.3. System of Equations with No Solution

3.4.4. To Identify the Number of Solutions of a System of Simultaneous Linear Equations

3.4.5. To Find the Value of the Unknown Variable When the Equation of the Two Lines is Given and their Graph is Described

3.4.6. Graph of Consistent and Inconsistent System of Linear Equations

3.4.7. Homogeneous System of Equations

3.5. Word Problems on Linear Equations in two variables

4. Quadratic Equations

4.1. Identify Quadratic Equations

4.2. Verify Solutions of a Quadratic Equation

4.3. Solve Quadratic Equations by Factorization

4.4. Solve Quadratic Equations by Completing the Square

4.5. Solve Quadratic Equations by Using Quadratic Formula

4.6. Nature of Roots of a Quadratic Equation

4.7. Word Problems on Quadratic Equations

5. Arithmetic Progressions

5.1. Tell if a Progression is an Arithmetic Progression (AP)

5.2. Find the First Term, Common Difference or the Next Term in an Arithmetic Progression (AP)

5.3. Find the Unknown Variable(s) in an Arithmetic Progression (AP)

5.4. Find the Numbers in AP Under Specified Conditions

5.5. General Term (n^th Term) of an Arithmetic Progression (AP)

5.5.1. Find the General Term of an Arithmetic Progression (AP)

5.5.2. Find the Number of Terms in an Arithmetic Progression (AP)

5.5.3. Find the Middle Term of an Arithmetic Progression

5.5.4. Find the Position of the Term of an Arithmetic Progression under Different Conditions (AP)

5.6. General Term (n^th Term) from the End of an Arithmetic Progression (AP)

5.7. Arithmetic Mean

5.8. Sum of n Terms of an Arithmetic Progression (AP)

5.8.1. Find the General Term of an Arithmetic Progression When the Sum of n Terms is Given (AP)

5.8.2. Find the Common Difference when the Sum of the Series is Given (AP) and the First and the Last Term is Given

5.8.3. Find the Number of Terms in an Arithmetic Progression (AP) When the Sum of the Series is Given

5.8.4. Find the Sum of an AP Under Different Conditions

5.9. Word Problems on Arithmetic Progressions (AP)

6. Triangles

6.1. Basic Proportionality Theorem (Thales's Theorem) and its Applications

6.2. Angle-Bisector Theorem and its Applications

6.3. Similar Triangles

6.3.1. Theorems and Problems Related to Similar Triangles

6.3.2. Ratio of the Areas of Two Similar Triangles

6.4. Pythagoras Theorem, Related Results and Problems

7. Coordinate Geometry

7.1. Distance Between Two Points

7.1.1. Find the Distance of the Given Point from the Origin

7.1.2. Find the Distance Between Two Given Points

7.1.3. Find the Coordinates of a Point Which is at a Fixed Distance from Another Point

7.1.4. Find a Point Equidistant from Two Given Points and Solve Related Problems

7.1.5. Find if the Given Points are Collinear and Solve Related Problems

7.2. Section Formula and Midpoint Formula

7.3. Centroid of a Triangle

7.4. Area of a Triangle

7.5. Area of a Parallelogram

8. Introduction to Trigonometry

8.1. Trigonometric Ratios

8.1.1. Trigonometric Ratios of an Acute Angle of a Right-Triangle

8.1.2. Reciprocal Relation Between Trigonometric Ratios

8.1.3. Quotient Relation of Trigonometric Ratios

8.1.4. If One Trigonometric Ratio (or evident) is known for an Angle, Find Other Trigonometric Ratios of that Angle

8.1.5. If One Trigonometric Ratio (or evident) is known for an Angle, Find Other Trigonometric Ratios of the Other Acute Angle in a Right-Triangle

8.1.6. If One Trigonometric Ratio is known (or evident) for an Angle, Evaluate Expressions Involving Other Trigonometric Ratios of that Angle

8.1.7. If One Trigonometric Ratio is known (or evident) for an Angle, Evaluate Expressions Involving Other Trigonometric Ratios of the Other Acute Angle in a Right-Triangle

8.1.8. Square Relation of Trigonometric Ratios

8.2. Trigonometric Ratios of Angles 0, 30, 45, 60, and 90 degrees

8.3. Trigonometric Ratios of Complementary Angles

8.4. Trigonometric Identities

8.4.1. Using Trigonometric Identities to Find the Value of the Expressions Involving Trigonometric Ratios

8.4.2. Elimination of Trigonometric Ratios Using Identities

9. Some Applications of Trigonometry

9.1. Heights and Distances

10. Circles

10.1. Theorems and Results Related to Tangents of Circles

11. Constructions

11.1. Division of a Line Segment

11.2. Construction of Triangles

11.3. Construction of Tangents to a Circle

12. Areas Related to Circle

12.1. Area and Circumference of a Circle

12.2. Area and Circumference of a Semi-Circle

12.3. Area and Circumference of a Circular Ring

12.4. Area of a Sector, Segment and Length of the Arc

12.5. Word Problems on Area Related to Circle

13. Surface Areas and Volumes

13.1. Volume and Surface Area of Solids

13.1.1. Volume and Surface Area of Cuboids and Cubes

13.1.2. Volume and Surface Area of Cylinders

13.1.3. Volume and Surface Area of Circular Cones

13.1.4. Volume and Surface Area of Conical Frustum

13.1.5. Volume and Surface Area of Spheres, Hemispheres and Spherical Shells

13.1.6. Conversion of Solid from One Shape to Another

13.1.7. Volume and Surface Area of Combination of Solids

13.1.8. Mixed Problems on Volume and Surface Area

14. Statistics

14.1. Mean of Grouped Data

14.1.1. Mean for an Exclusive Series

14.1.1.1. Direct Method

14.1.1.2. Assumed-Mean Method

14.1.1.3. Step-Deviation Method

14.1.2. Mean for an Inclusive Series

14.1.3. Word Problems on Mean

14.2. Median for Grouped Data

14.2.1. Median for an Exclusive Series

14.2.2. Median for an Inclusive Series

14.3. Mode of Grouped Data

14.3.1. Mode for an Exclusive Series

14.3.2. Mode for an Inclusive Series

14.3.3. Using Empirical Formula

14.4. Miscellaneous Questions on Mean, Mode and Median of Grouped Data

15. Probability

15.1. Card Problems

15.2. Dice Problems

15.3. Coin Problems

15.4. Other Problems

Class 10 NCERT (CBSE and ICSE) Basic Proportionality Theorem (Thales's Theorem) and its Applications

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