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Similarity

Maharashtra Board · Class 10 · Mathematics

Complete topic list for Similarity in Maharashtra Board Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions30 flashcards5 concepts

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4 Topics · Maharashtra Board Class 10 Mathematics

Topics in Similarity

1

1. Ratio of Areas of Two Triangles

  • Area of a triangle is half the product of base and height.
  • For any two triangles, the ratio of their areas equals the ratio of the products of their bases and corresponding heights.
  • If two triangles have equal heights, the ratio of their areas equals the ratio of their corresponding bases.
2

2. Basic Proportionality Theorem and Its Converse

  • The Basic Proportionality Theorem states that a line parallel to one side of a triangle, intersecting the other two sides at distinct points, divides those sides in the same proportion.
  • In the standard proof, the triangles formed by the construction are compared through equal heights and equal bases.
  • The converse of BPT states that if a line divides two sides of a triangle in the same ratio, then it is parallel to the third side.
3

3. Angle Bisector Theorem and Its Converse

  • An angle bisector of a triangle divides the opposite side in the ratio of the remaining two sides.
  • In the proof, CB is shown congruent to CD using the isosceles triangle property.
  • The construction uses a line parallel to the bisector ray through the opposite vertex.
4

4. Three Parallel Lines and Their Transversals

  • Three parallel lines cut two transversals into intercepts that are proportional to each other.
  • The theorem compares intercepts on one transversal with the corresponding intercepts on another transversal.
  • The proof uses a constructed segment PC meeting the middle parallel line at an auxiliary point D.

Key Concepts

Central concept: Similarity of triangles and its key properties, tests, and theorems

Ratio of areas of two trianglesBasic proportionality theoremConverse of basic proportionality theoremAngle bisector theoremConverse of angle bisector theoremThree parallel lines and transversalsSimilarity of trianglesTests of similarity

Frequently Asked Questions

What are the important topics in Similarity for Maharashtra Board Class 10 Mathematics?
Similarity covers several key topics that are frequently asked in Maharashtra Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Similarity — Maharashtra Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Similarity

All 13 chapters — Maharashtra Board Class 10 Mathematics Syllabus

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