Table of contents |
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Introduction |
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Locus and Its Constructions |
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Theorems Based on Symmetry |
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Applications |
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Summary |
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Imagine a point moving through space, tracing a path as it follows specific rules—like staying the same distance from two lines or circling around a fixed point! This fascinating concept is called a locus, and in this chapter, we dive into the exciting world of loci and their constructions. From straight lines to circles, we'll explore how points move to create unique shapes based on given conditions. Get ready to uncover the secrets of loci, understand their properties, and learn how to construct them step by step using rulers and compasses. Let’s embark on this geometric adventure and see how loci bring mathematics to life!
Example: Two parallel lines l and s are 4 cm apart. Find the locus of a point always equidistant from both lines.
Process:
Example: Show the locus of a point equidistant from a fixed point is a circle with the fixed point as the center.
Theorem 3: The locus of a point equidistant from two intersecting lines is the bisector of the angles between them.
Steps to understand:
Theorem 4: The locus of a point equidistant from two fixed points is the perpendicular bisector of the line joining them.Steps to understand:
Concept: Loci are used to find points satisfying specific geometric conditions in triangles, quadrilaterals, etc.
Steps to apply:
Example: In triangle ABC, BX bisects ∠ABC and intersects AC at D. Line CY is perpendicular to AB and intersects BX at P, where Y is the midpoint of AB. Prove: (i) P is equidistant from A and B, (ii) D is equidistant from AB and BC.
Example: A and B are two fixed points. Draw the locus of point P such that ∠APB = 90°.
Centroid:Centroid Properties
Incentre:
Circumcentre:
Orthocentre:
Isosceles Triangle Properties:
Equilateral Triangle Properties:
Example:
74 videos|328 docs|30 tests
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1. What is the definition of a locus in geometry? | ![]() |
2. What are some key theorems based on symmetry in relation to loci? | ![]() |
3. How can loci be applied in real-life situations? | ![]() |
4. What are some common constructions involving loci? | ![]() |
5. What is the importance of studying loci in Class 10 mathematics? | ![]() |